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 A286929 #15 May 24 2018 09:26:56
%S A286929 1,1,2,3,4,6,9,13,17,25,33,46,61,84,108,147,187,248,316,414,519,675,
%T A286929 843,1077,1339,1699,2090,2633,3227,4020,4909,6076,7369,9075,10965,
%U A286929 13394,16129,19613,23493,28434,33954,40858,48643,58301,69124,82547,97593,116017,136804,162101,190504
%N A286929 Number of partitions of n such that each part is no more than 3 more than the sum of all smaller parts.
%C A286929 Generalization of Adams-Watters's criterion for complete partitions, that each part is no more than 1 more than the sum of all smaller parts.
%C A286929 Also the number of complete partitions of n+1 that contain more than one 1. - _George Beck_, Oct 01 2017
%H A286929 Alois P. Heinz, <a href="/A286929/b286929.txt">Table of n, a(n) for n = 0..10000</a>
%F A286929 a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*sqrt(3)*n). - _Vaclav Kotesovec_, May 24 2018
%e A286929 For n = 8, a(8) = 17 counts all partitions of 8 except (8), (7,1), (6,2), (6,1,1), and (4,4).
%t A286929 Table[Count[IntegerPartitions@ n, w_ /; And[Last@ w <= 3, NoneTrue[w - Rest@ PadRight[3 + Reverse@ Accumulate@ Reverse@ w, Length@ w + 1, Last@ w], # > 0 &]]], {n, 50}] (* _Michael De Vlieger_, May 16 2017, Version 10 *)
%Y A286929 Cf. A126796.
%K A286929 nonn
%O A286929 0,3
%A A286929 _Brian Hopkins_, May 16 2017