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 A286097 #30 May 24 2018 09:30:38
%S A286097 1,1,2,3,5,6,10,13,20,26,37,48,68,86,119,152,204,258,342,428,560,698,
%T A286097 897,1114,1421,1748,2210,2712,3390,4140,5140,6240,7702,9314,11402,
%U A286097 13741,16742,20071,24333,29087,35056,41770,50137,59503,71148,84195,100213,118275,140307,165041,195139
%N A286097 Number of partitions of n such that each part is no more than 4 more than the sum of all smaller parts.
%C A286097 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.
%H A286097 Alois P. Heinz, <a href="/A286097/b286097.txt">Table of n, a(n) for n = 0..10000</a>
%F A286097 a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*sqrt(3)*n). - _Vaclav Kotesovec_, May 24 2018
%e A286097 For n = 8, a(8) = 20 counts all partitions of 8 except (8) and (7,1).
%t A286097 Table[Count[IntegerPartitions@n, w_ /; And[Last@w <= 4, NoneTrue[ w - Rest@ PadRight[4 + Reverse@Accumulate@Reverse@w, Length@w + 1, Last@w], # > 0 &]]], {n, 50}] (* _George Beck_, May 17 2017, Version 11.1.1, adapted from A286929 *)
%Y A286097 Cf. A126796.
%K A286097 nonn
%O A286097 0,3
%A A286097 _Brian Hopkins_, May 16 2017