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 A357849 #8 Nov 02 2022 11:52:59
%S A357849 0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,0,1,1,1,1,0,1,1,1,1,1,1,1,2,
%T A357849 1,1,1,1,2,1,1,2,1,2,2,1,2,1,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,3,2,
%U A357849 3,2,2,3,2,3,3,2,3,3,3,3,2,3,3,3,3,3,3
%N A357849 Number of integer partitions (w,x,y) summing to n such that 2w = 3x + 4y.
%e A357849 The partitions for n = 34, 64, 89, 119, 144:
%e A357849 (21,10,3) (39,22,3) (54,32,3) (72,44,3) (87,54,3)
%e A357849 (40,16,8) (55,26,8) (73,38,8) (88,48,8)
%e A357849 (56,20,13) (74,32,13) (89,42,13)
%e A357849 (75,26,18) (90,36,18)
%e A357849 (91,30,23)
%t A357849 Table[Length[Select[IntegerPartitions[n,{3}],2*#[[1]]==3*#[[2]]+4*#[[3]]&]],{n,0,100}]
%o A357849 (Python)
%o A357849 def A357849(n): return sum(1 for y in range(1,n-1) if (m:=2*n-6*y)>=5*y and 5*(n-y)>=2*m and m%5==0) # _Chai Wah Wu_, Nov 02 2022
%Y A357849 Partitions are counted by A000041, strict A000009.
%Y A357849 The ordered version appears to be A008676, ranked by A357489.
%Y A357849 These partitions are ranked by A358102.
%K A357849 nonn
%O A357849 0,34
%A A357849 _Gus Wiseman_, Nov 02 2022