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, 7) partitions with addends ≥ 7.

Partitions that have 7 as the smallest addend are marked in gray.
For n ≥ 14 their number is A026807(n−7, 7).
Visually this means that there are 7 other partitions over every topmost gray one - apart from first partition in the table.

Two partitions in the same column that are 7 rows apart differ by exactly one addend 7.
7 0
(7, 1) 14
7: 1
8 1
(8, 1) 21
8: 1
9 2
(9, 1) 29
9: 1
10 3
(10, 1) 41
10: 1
11 4
(11, 1) 55
11: 1
12 5
(12, 1) 76
12: 1
13 6
(13, 1) 100
13: 1
14 0
(14, 1) 133
7: 2
(14, 2) 134
14: 1
15 1
(15, 1) 174
8: 1,
7: 1
(15, 2) 175
15: 1
16 2
(16, 1) 228
9: 1,
7: 1
(16, 2) 229
8: 2
(16, 3) 230
16: 1
17 3
(17, 1) 294
10: 1,
7: 1
(17, 2) 295
9: 1,
8: 1
(17, 3) 296
17: 1
18 4
(18, 1) 381
11: 1,
7: 1
(18, 2) 382
10: 1,
8: 1
(18, 3) 383
9: 2
(18, 4) 384
18: 1
19 5
(19, 1) 486
12: 1,
7: 1
(19, 2) 487
11: 1,
8: 1
(19, 3) 488
10: 1,
9: 1
(19, 4) 489
19: 1
20 6
(20, 1) 622
13: 1,
7: 1
(20, 2) 623
12: 1,
8: 1
(20, 3) 624
11: 1,
9: 1
(20, 4) 625
10: 2
(20, 5) 626
20: 1
21 0
(21, 1) 786
7: 3
(21, 2) 787
14: 1,
7: 1
(21, 3) 788
13: 1,
8: 1
(21, 4) 789
12: 1,
9: 1
(21, 5) 790
11: 1,
10: 1
(21, 6) 791
21: 1
22 1
(22, 1) 995
8: 1,
7: 2
(22, 2) 996
15: 1,
7: 1
(22, 3) 997
14: 1,
8: 1
(22, 4) 998
13: 1,
9: 1
(22, 5) 999
12: 1,
10: 1
(22, 6) 1000
11: 2
(22, 7) 1001
22: 1
23 2
(23, 1) 1247
9: 1,
7: 2
(23, 2) 1248
8: 2,
7: 1
(23, 3) 1249
16: 1,
7: 1
(23, 4) 1250
15: 1,
8: 1
(23, 5) 1251
14: 1,
9: 1
(23, 6) 1252
13: 1,
10: 1
(23, 7) 1253
12: 1,
11: 1
(23, 8) 1254
23: 1
24 3
(24, 1) 1565
10: 1,
7: 2
(24, 2) 1566
9: 1,
8: 1,
7: 1
(24, 3) 1567
17: 1,
7: 1
(24, 4) 1568
8: 3
(24, 5) 1569
16: 1,
8: 1
(24, 6) 1570
15: 1,
9: 1
(24, 7) 1571
14: 1,
10: 1
(24, 8) 1572
13: 1,
11: 1
(24, 9) 1573
12: 2
(24, 10) 1574
24: 1
25 4
(25, 1) 1947
11: 1,
7: 2
(25, 2) 1948
10: 1,
8: 1,
7: 1
(25, 3) 1949
9: 2,
7: 1
(25, 4) 1950
18: 1,
7: 1
(25, 5) 1951
9: 1,
8: 2
(25, 6) 1952
17: 1,
8: 1
(25, 7) 1953
16: 1,
9: 1
(25, 8) 1954
15: 1,
10: 1
(25, 9) 1955
14: 1,
11: 1
(25, 10) 1956
13: 1,
12: 1
(25, 11) 1957
25: 1
26 5
(26, 1) 2423
12: 1,
7: 2
(26, 2) 2424
11: 1,
8: 1,
7: 1
(26, 3) 2425
10: 1,
9: 1,
7: 1
(26, 4) 2426
19: 1,
7: 1
(26, 5) 2427
10: 1,
8: 2
(26, 6) 2428
9: 2,
8: 1
(26, 7) 2429
18: 1,
8: 1
(26, 8) 2430
17: 1,
9: 1
(26, 9) 2431
16: 1,
10: 1
(26, 10) 2432
15: 1,
11: 1
(26, 11) 2433
14: 1,
12: 1
(26, 12) 2434
13: 2
(26, 13) 2435
26: 1
27 6
(27, 1) 2995
13: 1,
7: 2
(27, 2) 2996
12: 1,
8: 1,
7: 1
(27, 3) 2997
11: 1,
9: 1,
7: 1
(27, 4) 2998
10: 2,
7: 1
(27, 5) 2999
20: 1,
7: 1
(27, 6) 3000
11: 1,
8: 2
(27, 7) 3001
10: 1,
9: 1,
8: 1
(27, 8) 3002
19: 1,
8: 1
(27, 9) 3003
9: 3
(27, 10) 3004
18: 1,
9: 1
(27, 11) 3005
17: 1,
10: 1
(27, 12) 3006
16: 1,
11: 1
(27, 13) 3007
15: 1,
12: 1
(27, 14) 3008
14: 1,
13: 1
(27, 15) 3009
27: 1
28 0
(28, 1) 3700
7: 4
(28, 2) 3701
14: 1,
7: 2
(28, 3) 3702
13: 1,
8: 1,
7: 1
(28, 4) 3703
12: 1,
9: 1,
7: 1
(28, 5) 3704
11: 1,
10: 1,
7: 1
(28, 6) 3705
21: 1,
7: 1
(28, 7) 3706
12: 1,
8: 2
(28, 8) 3707
11: 1,
9: 1,
8: 1
(28, 9) 3708
10: 2,
8: 1
(28, 10) 3709
20: 1,
8: 1
(28, 11) 3710
10: 1,
9: 2
(28, 12) 3711
19: 1,
9: 1
(28, 13) 3712
18: 1,
10: 1
(28, 14) 3713
17: 1,
11: 1
(28, 15) 3714
16: 1,
12: 1
(28, 16) 3715
15: 1,
13: 1
(28, 17) 3716
14: 2
(28, 18) 3717
28: 1
29 1
(29, 1) 4545
8: 1,
7: 3
(29, 2) 4546
15: 1,
7: 2
(29, 3) 4547
14: 1,
8: 1,
7: 1
(29, 4) 4548
13: 1,
9: 1,
7: 1
(29, 5) 4549
12: 1,
10: 1,
7: 1
(29, 6) 4550
11: 2,
7: 1
(29, 7) 4551
22: 1,
7: 1
(29, 8) 4552
13: 1,
8: 2
(29, 9) 4553
12: 1,
9: 1,
8: 1
(29, 10) 4554
11: 1,
10: 1,
8: 1
(29, 11) 4555
21: 1,
8: 1
(29, 12) 4556
11: 1,
9: 2
(29, 13) 4557
10: 2,
9: 1
(29, 14) 4558
20: 1,
9: 1
(29, 15) 4559
19: 1,
10: 1
(29, 16) 4560
18: 1,
11: 1
(29, 17) 4561
17: 1,
12: 1
(29, 18) 4562
16: 1,
13: 1
(29, 19) 4563
15: 1,
14: 1
(29, 20) 4564
29: 1
30 2
(30, 1) 5580
9: 1,
7: 3
(30, 2) 5581
8: 2,
7: 2
(30, 3) 5582
16: 1,
7: 2
(30, 4) 5583
15: 1,
8: 1,
7: 1
(30, 5) 5584
14: 1,
9: 1,
7: 1
(30, 6) 5585
13: 1,
10: 1,
7: 1
(30, 7) 5586
12: 1,
11: 1,
7: 1
(30, 8) 5587
23: 1,
7: 1
(30, 9) 5588
14: 1,
8: 2
(30, 10) 5589
13: 1,
9: 1,
8: 1
(30, 11) 5590
12: 1,
10: 1,
8: 1
(30, 12) 5591
11: 2,
8: 1
(30, 13) 5592
22: 1,
8: 1
(30, 14) 5593
12: 1,
9: 2
(30, 15) 5594
11: 1,
10: 1,
9: 1
(30, 16) 5595
21: 1,
9: 1
(30, 17) 5596
10: 3
(30, 18) 5597
20: 1,
10: 1
(30, 19) 5598
19: 1,
11: 1
(30, 20) 5599
18: 1,
12: 1
(30, 21) 5600
17: 1,
13: 1
(30, 22) 5601
16: 1,
14: 1
(30, 23) 5602
15: 2
(30, 24) 5603
30: 1