Partitions as integers
(A194602)
thin fat 		Partitions with addends ≥
2 3 4 5 6 7 8 		Numbers of partitions of n with addends ≥ k
(A026807)
full half
Row n of this triangle contains the A026807(n, 6) partitions with addends ≥ 6.

Partitions that have 6 as the smallest addend are marked in gray.
For n ≥ 12 their number is A026807(n−6, 6).
Visually this means that there are 6 other partitions over every topmost gray one - apart from first partition in the table.

Two partitions in the same column that are 6 rows apart differ by exactly one addend 6.
6 0
(6, 1) 10
6: 1
7 1
(7, 1) 14
7: 1
8 2
(8, 1) 21
8: 1
9 3
(9, 1) 29
9: 1
10 4
(10, 1) 41
10: 1
11 5
(11, 1) 55
11: 1
12 0
(12, 1) 75
6: 2
(12, 2) 76
12: 1
13 1
(13, 1) 99
7: 1,
6: 1
(13, 2) 100
13: 1
14 2
(14, 1) 132
8: 1,
6: 1
(14, 2) 133
7: 2
(14, 3) 134
14: 1
15 3
(15, 1) 173
9: 1,
6: 1
(15, 2) 174
8: 1,
7: 1
(15, 3) 175
15: 1
16 4
(16, 1) 227
10: 1,
6: 1
(16, 2) 228
9: 1,
7: 1
(16, 3) 229
8: 2
(16, 4) 230
16: 1
17 5
(17, 1) 293
11: 1,
6: 1
(17, 2) 294
10: 1,
7: 1
(17, 3) 295
9: 1,
8: 1
(17, 4) 296
17: 1
18 0
(18, 1) 379
6: 3
(18, 2) 380
12: 1,
6: 1
(18, 3) 381
11: 1,
7: 1
(18, 4) 382
10: 1,
8: 1
(18, 5) 383
9: 2
(18, 6) 384
18: 1
19 1
(19, 1) 484
7: 1,
6: 2
(19, 2) 485
13: 1,
6: 1
(19, 3) 486
12: 1,
7: 1
(19, 4) 487
11: 1,
8: 1
(19, 5) 488
10: 1,
9: 1
(19, 6) 489
19: 1
20 2
(20, 1) 619
8: 1,
6: 2
(20, 2) 620
7: 2,
6: 1
(20, 3) 621
14: 1,
6: 1
(20, 4) 622
13: 1,
7: 1
(20, 5) 623
12: 1,
8: 1
(20, 6) 624
11: 1,
9: 1
(20, 7) 625
10: 2
(20, 8) 626
20: 1
21 3
(21, 1) 783
9: 1,
6: 2
(21, 2) 784
8: 1,
7: 1,
6: 1
(21, 3) 785
15: 1,
6: 1
(21, 4) 786
7: 3
(21, 5) 787
14: 1,
7: 1
(21, 6) 788
13: 1,
8: 1
(21, 7) 789
12: 1,
9: 1
(21, 8) 790
11: 1,
10: 1
(21, 9) 791
21: 1
22 4
(22, 1) 991
10: 1,
6: 2
(22, 2) 992
9: 1,
7: 1,
6: 1
(22, 3) 993
8: 2,
6: 1
(22, 4) 994
16: 1,
6: 1
(22, 5) 995
8: 1,
7: 2
(22, 6) 996
15: 1,
7: 1
(22, 7) 997
14: 1,
8: 1
(22, 8) 998
13: 1,
9: 1
(22, 9) 999
12: 1,
10: 1
(22, 10) 1000
11: 2
(22, 11) 1001
22: 1
23 5
(23, 1) 1243
11: 1,
6: 2
(23, 2) 1244
10: 1,
7: 1,
6: 1
(23, 3) 1245
9: 1,
8: 1,
6: 1
(23, 4) 1246
17: 1,
6: 1
(23, 5) 1247
9: 1,
7: 2
(23, 6) 1248
8: 2,
7: 1
(23, 7) 1249
16: 1,
7: 1
(23, 8) 1250
15: 1,
8: 1
(23, 9) 1251
14: 1,
9: 1
(23, 10) 1252
13: 1,
10: 1
(23, 11) 1253
12: 1,
11: 1
(23, 12) 1254
23: 1
24 0
(24, 1) 1559
6: 4
(24, 2) 1560
12: 1,
6: 2
(24, 3) 1561
11: 1,
7: 1,
6: 1
(24, 4) 1562
10: 1,
8: 1,
6: 1
(24, 5) 1563
9: 2,
6: 1
(24, 6) 1564
18: 1,
6: 1
(24, 7) 1565
10: 1,
7: 2
(24, 8) 1566
9: 1,
8: 1,
7: 1
(24, 9) 1567
17: 1,
7: 1
(24, 10) 1568
8: 3
(24, 11) 1569
16: 1,
8: 1
(24, 12) 1570
15: 1,
9: 1
(24, 13) 1571
14: 1,
10: 1
(24, 14) 1572
13: 1,
11: 1
(24, 15) 1573
12: 2
(24, 16) 1574
24: 1
25 1
(25, 1) 1941
7: 1,
6: 3
(25, 2) 1942
13: 1,
6: 2
(25, 3) 1943
12: 1,
7: 1,
6: 1
(25, 4) 1944
11: 1,
8: 1,
6: 1
(25, 5) 1945
10: 1,
9: 1,
6: 1
(25, 6) 1946
19: 1,
6: 1
(25, 7) 1947
11: 1,
7: 2
(25, 8) 1948
10: 1,
8: 1,
7: 1
(25, 9) 1949
9: 2,
7: 1
(25, 10) 1950
18: 1,
7: 1
(25, 11) 1951
9: 1,
8: 2
(25, 12) 1952
17: 1,
8: 1
(25, 13) 1953
16: 1,
9: 1
(25, 14) 1954
15: 1,
10: 1
(25, 15) 1955
14: 1,
11: 1
(25, 16) 1956
13: 1,
12: 1
(25, 17) 1957
25: 1
26 2
(26, 1) 2415
8: 1,
6: 3
(26, 2) 2416
7: 2,
6: 2
(26, 3) 2417
14: 1,
6: 2
(26, 4) 2418
13: 1,
7: 1,
6: 1
(26, 5) 2419
12: 1,
8: 1,
6: 1
(26, 6) 2420
11: 1,
9: 1,
6: 1
(26, 7) 2421
10: 2,
6: 1
(26, 8) 2422
20: 1,
6: 1
(26, 9) 2423
12: 1,
7: 2
(26, 10) 2424
11: 1,
8: 1,
7: 1
(26, 11) 2425
10: 1,
9: 1,
7: 1
(26, 12) 2426
19: 1,
7: 1
(26, 13) 2427
10: 1,
8: 2
(26, 14) 2428
9: 2,
8: 1
(26, 15) 2429
18: 1,
8: 1
(26, 16) 2430
17: 1,
9: 1
(26, 17) 2431
16: 1,
10: 1
(26, 18) 2432
15: 1,
11: 1
(26, 19) 2433
14: 1,
12: 1
(26, 20) 2434
13: 2
(26, 21) 2435
26: 1
27 3
(27, 1) 2986
9: 1,
6: 3
(27, 2) 2987
8: 1,
7: 1,
6: 2
(27, 3) 2988
15: 1,
6: 2
(27, 4) 2989
7: 3,
6: 1
(27, 5) 2990
14: 1,
7: 1,
6: 1
(27, 6) 2991
13: 1,
8: 1,
6: 1
(27, 7) 2992
12: 1,
9: 1,
6: 1
(27, 8) 2993
11: 1,
10: 1,
6: 1
(27, 9) 2994
21: 1,
6: 1
(27, 10) 2995
13: 1,
7: 2
(27, 11) 2996
12: 1,
8: 1,
7: 1
(27, 12) 2997
11: 1,
9: 1,
7: 1
(27, 13) 2998
10: 2,
7: 1
(27, 14) 2999
20: 1,
7: 1
(27, 15) 3000
11: 1,
8: 2
(27, 16) 3001
10: 1,
9: 1,
8: 1
(27, 17) 3002
19: 1,
8: 1
(27, 18) 3003
9: 3
(27, 19) 3004
18: 1,
9: 1
(27, 20) 3005
17: 1,
10: 1
(27, 21) 3006
16: 1,
11: 1
(27, 22) 3007
15: 1,
12: 1
(27, 23) 3008
14: 1,
13: 1
(27, 24) 3009
27: 1
28 4
(28, 1) 3689
10: 1,
6: 3
(28, 2) 3690
9: 1,
7: 1,
6: 2
(28, 3) 3691
8: 2,
6: 2
(28, 4) 3692
16: 1,
6: 2
(28, 5) 3693
8: 1,
7: 2,
6: 1
(28, 6) 3694
15: 1,
7: 1,
6: 1
(28, 7) 3695
14: 1,
8: 1,
6: 1
(28, 8) 3696
13: 1,
9: 1,
6: 1
(28, 9) 3697
12: 1,
10: 1,
6: 1
(28, 10) 3698
11: 2,
6: 1
(28, 11) 3699
22: 1,
6: 1
(28, 12) 3700
7: 4
(28, 13) 3701
14: 1,
7: 2
(28, 14) 3702
13: 1,
8: 1,
7: 1
(28, 15) 3703
12: 1,
9: 1,
7: 1
(28, 16) 3704
11: 1,
10: 1,
7: 1
(28, 17) 3705
21: 1,
7: 1
(28, 18) 3706
12: 1,
8: 2
(28, 19) 3707
11: 1,
9: 1,
8: 1
(28, 20) 3708
10: 2,
8: 1
(28, 21) 3709
20: 1,
8: 1
(28, 22) 3710
10: 1,
9: 2
(28, 23) 3711
19: 1,
9: 1
(28, 24) 3712
18: 1,
10: 1
(28, 25) 3713
17: 1,
11: 1
(28, 26) 3714
16: 1,
12: 1
(28, 27) 3715
15: 1,
13: 1
(28, 28) 3716
14: 2
(28, 29) 3717
28: 1
29 5
(29, 1) 4533
11: 1,
6: 3
(29, 2) 4534
10: 1,
7: 1,
6: 2
(29, 3) 4535
9: 1,
8: 1,
6: 2
(29, 4) 4536
17: 1,
6: 2
(29, 5) 4537
9: 1,
7: 2,
6: 1
(29, 6) 4538
8: 2,
7: 1,
6: 1
(29, 7) 4539
16: 1,
7: 1,
6: 1
(29, 8) 4540
15: 1,
8: 1,
6: 1
(29, 9) 4541
14: 1,
9: 1,
6: 1
(29, 10) 4542
13: 1,
10: 1,
6: 1
(29, 11) 4543
12: 1,
11: 1,
6: 1
(29, 12) 4544
23: 1,
6: 1
(29, 13) 4545
8: 1,
7: 3
(29, 14) 4546
15: 1,
7: 2
(29, 15) 4547
14: 1,
8: 1,
7: 1
(29, 16) 4548
13: 1,
9: 1,
7: 1
(29, 17) 4549
12: 1,
10: 1,
7: 1
(29, 18) 4550
11: 2,
7: 1
(29, 19) 4551
22: 1,
7: 1
(29, 20) 4552
13: 1,
8: 2
(29, 21) 4553
12: 1,
9: 1,
8: 1
(29, 22) 4554
11: 1,
10: 1,
8: 1
(29, 23) 4555
21: 1,
8: 1
(29, 24) 4556
11: 1,
9: 2
(29, 25) 4557
10: 2,
9: 1
(29, 26) 4558
20: 1,
9: 1
(29, 27) 4559
19: 1,
10: 1
(29, 28) 4560
18: 1,
11: 1
(29, 29) 4561
17: 1,
12: 1
(29, 30) 4562
16: 1,
13: 1
(29, 31) 4563
15: 1,
14: 1
(29, 32) 4564
29: 1
30 0
(30, 1) 5564
6: 5
(30, 2) 5565
12: 1,
6: 3
(30, 3) 5566
11: 1,
7: 1,
6: 2
(30, 4) 5567
10: 1,
8: 1,
6: 2
(30, 5) 5568
9: 2,
6: 2
(30, 6) 5569
18: 1,
6: 2
(30, 7) 5570
10: 1,
7: 2,
6: 1
(30, 8) 5571
9: 1,
8: 1,
7: 1,
6: 1
(30, 9) 5572
17: 1,
7: 1,
6: 1
(30, 10) 5573
8: 3,
6: 1
(30, 11) 5574
16: 1,
8: 1,
6: 1
(30, 12) 5575
15: 1,
9: 1,
6: 1
(30, 13) 5576
14: 1,
10: 1,
6: 1
(30, 14) 5577
13: 1,
11: 1,
6: 1
(30, 15) 5578
12: 2,
6: 1
(30, 16) 5579
24: 1,
6: 1
(30, 17) 5580
9: 1,
7: 3
(30, 18) 5581
8: 2,
7: 2
(30, 19) 5582
16: 1,
7: 2
(30, 20) 5583
15: 1,
8: 1,
7: 1
(30, 21) 5584
14: 1,
9: 1,
7: 1
(30, 22) 5585
13: 1,
10: 1,
7: 1
(30, 23) 5586
12: 1,
11: 1,
7: 1
(30, 24) 5587
23: 1,
7: 1
(30, 25) 5588
14: 1,
8: 2
(30, 26) 5589
13: 1,
9: 1,
8: 1
(30, 27) 5590
12: 1,
10: 1,
8: 1
(30, 28) 5591
11: 2,
8: 1
(30, 29) 5592
22: 1,
8: 1
(30, 30) 5593
12: 1,
9: 2
(30, 31) 5594
11: 1,
10: 1,
9: 1
(30, 32) 5595
21: 1,
9: 1
(30, 33) 5596
10: 3
(30, 34) 5597
20: 1,
10: 1
(30, 35) 5598
19: 1,
11: 1
(30, 36) 5599
18: 1,
12: 1
(30, 37) 5600
17: 1,
13: 1
(30, 38) 5601
16: 1,
14: 1
(30, 39) 5602
15: 2
(30, 40) 5603
30: 1