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 A342094 #17 Feb 01 2022 05:12:22
%S A342094 1,2,3,4,5,8,9,13,16,21,27,37,44,59,75,94,117,153,186,238,296,369,458,
%T A342094 573,701,870,1068,1312,1601,1964,2384,2907,3523,4270,5159,6235,7491,
%U A342094 9021,10819,12964,15494,18517,22049,26260,31195,37020,43851,51906,61290
%N A342094 Number of integer partitions of n with no adjacent parts having quotient > 2.
%C A342094 The decapitation of such a partition (delete the greatest part) is term-wise greater than or equal to its negated first-differences.
%H A342094 Fausto A. C. Cariboni, <a href="/A342094/b342094.txt">Table of n, a(n) for n = 1..250</a>
%e A342094 The a(1) = 1 through a(8) = 13 partitions:
%e A342094 (1) (2) (3) (4) (5) (6) (7) (8)
%e A342094 (11) (21) (22) (32) (33) (43) (44)
%e A342094 (111) (211) (221) (42) (322) (53)
%e A342094 (1111) (2111) (222) (421) (332)
%e A342094 (11111) (321) (2221) (422)
%e A342094 (2211) (3211) (2222)
%e A342094 (21111) (22111) (3221)
%e A342094 (111111) (211111) (4211)
%e A342094 (1111111) (22211)
%e A342094 (32111)
%e A342094 (221111)
%e A342094 (2111111)
%e A342094 (11111111)
%t A342094 Table[Length[Select[IntegerPartitions[n],And@@Thread[Differences[-#]<=Rest[#]]&]],{n,30}]
%Y A342094 The version with no adjacent parts having quotient < 2 is A000929.
%Y A342094 The case of equality (all adjacent parts having quotient 2) is A154402.
%Y A342094 A strong multiplicative version is A342083 or A342084.
%Y A342094 The multiplicative version is A342085, with reciprocal version A337135.
%Y A342094 The strict case is A342095.
%Y A342094 The version with all adjacent parts having quotient < 2 is A342096, with strict case A342097.
%Y A342094 The version with all adjacent parts having quotient > 2 is A342098.
%Y A342094 The Heinz numbers of these partitions are listed by A342191.
%Y A342094 A000009 counts strict partitions.
%Y A342094 A003114 counts partitions with adjacent parts differing by more than 1.
%Y A342094 A034296 counts partitions with adjacent parts differing by at most 1.
%Y A342094 A038548 counts inferior (or superior) divisors, listed by A161906.
%Y A342094 A161908 lists superior prime divisors.
%Y A342094 Cf. A001055, A001227, A003242, A027193, A167606, A178470, A253784, A341591.
%K A342094 nonn
%O A342094 1,2
%A A342094 _Gus Wiseman_, Mar 02 2021