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 A325690 #14 Feb 19 2022 20:28:03
%S A325690 0,0,0,1,0,2,2,4,3,7,6,10,9,14,13,19,17,24,23,30,28,37,35,44,42,52,50,
%T A325690 61,58,70,68,80,77,91,88,102,99,114,111,127,123,140,137,154,150,169,
%U A325690 165,184,180,200,196,217,212,234,230,252,247,271,266,290,285,310
%N A325690 Number of length-3 integer partitions of n whose largest part is not the sum of the other two.
%C A325690 Confirmed recurrence relation from _Colin Barker_ for n <= 10000. - _Fausto A. C. Cariboni_, Feb 19 2022
%H A325690 Fausto A. C. Cariboni, <a href="/A325690/b325690.txt">Table of n, a(n) for n = 0..10000</a>
%F A325690 Conjectures from _Colin Barker_, May 15 2019: (Start)
%F A325690 G.f.: x^3*(1 + x^2 + x^3 + x^4) / ((1 - x)^3*(1 + x)^2*(1 + x^2)*(1 + x + x^2)).
%F A325690 a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-5) - a(n-6) - a(n-7) + a(n-9) for n>8.
%F A325690 (End)
%e A325690 The a(3) = 1 through a(13) = 14 partitions (A = 10, B = 11):
%e A325690 (111) (221) (222) (322) (332) (333) (433) (443) (444) (544)
%e A325690 (311) (411) (331) (521) (432) (442) (533) (543) (553)
%e A325690 (421) (611) (441) (622) (542) (552) (643)
%e A325690 (511) (522) (631) (551) (732) (652)
%e A325690 (531) (721) (632) (741) (661)
%e A325690 (621) (811) (641) (822) (733)
%e A325690 (711) (722) (831) (742)
%e A325690 (731) (921) (751)
%e A325690 (821) (A11) (832)
%e A325690 (911) (841)
%e A325690 (922)
%e A325690 (931)
%e A325690 (A21)
%e A325690 (B11)
%t A325690 Table[Length[Select[IntegerPartitions[n,{3}],#[[1]]!=#[[2]]+#[[3]]&]],{n,0,30}]
%Y A325690 Column k = 3 of A325592.
%Y A325690 Cf. A000041, A001399, A005044, A008642, A069905, A266223.
%Y A325690 Cf. A325689, A325691, A325694.
%K A325690 nonn
%O A325690 0,6
%A A325690 _Gus Wiseman_, May 15 2019