This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342098 #9 Jan 26 2022 08:28:05
%S A342098 1,1,1,2,2,2,3,3,3,4,5,5,6,7,7,8,9,10,11,12,13,14,15,16,18,20,21,23,
%T A342098 25,26,28,31,33,35,38,40,42,45,48,51,55,58,61,65,68,72,77,81,85,90,94,
%U A342098 98,104,109,114,121,127,132,139,146
%N A342098 Number of (necessarily strict) integer partitions of n with all adjacent parts having quotients > 2.
%C A342098 The decapitation of such a partition (delete the greatest part) is term-wise less than its negated first-differences.
%H A342098 Fausto A. C. Cariboni, <a href="/A342098/b342098.txt">Table of n, a(n) for n = 1..3000</a>
%e A342098 The a(1) = 1 through a(16) = 8 partitions (A..G = 10..16):
%e A342098 1 2 3 4 5 6 7 8 9 A B C D E F G
%e A342098 31 41 51 52 62 72 73 83 93 94 A4 B4 B5
%e A342098 61 71 81 82 92 A2 A3 B3 C3 C4
%e A342098 91 A1 B1 B2 C2 D2 D3
%e A342098 731 831 C1 D1 E1 E2
%e A342098 931 941 A41 F1
%e A342098 A31 B31 B41
%e A342098 C31
%t A342098 Table[Length[Select[IntegerPartitions[n],And@@Thread[Differences[-#]>Rest[#]]&]],{n,30}]
%Y A342098 The version allowing equality is A000929.
%Y A342098 The case of equality (all adjacent parts having quotient 2) is A154402.
%Y A342098 The multiplicative version is A342083.
%Y A342098 The version with all quotients <= 2 is A342094 (strict: A342095).
%Y A342098 The version with all quotients < 2 is A342096 (strict: A342097).
%Y A342098 A000009 counts strict partitions.
%Y A342098 A003114 counts partitions with adjacent parts differing by more than 1.
%Y A342098 A034296 counts partitions with adjacent parts differing by at most 1.
%Y A342098 Cf. A027193, A001055, A001227, A003242, A167606, A178470, A337135, A342084, A342085.
%K A342098 nonn
%O A342098 1,4
%A A342098 _Gus Wiseman_, Mar 04 2021