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 A353501 #12 May 17 2022 17:47:27
%S A353501 1,0,0,0,0,0,0,0,0,1,0,0,2,0,0,2,1,0,2,0,2,3,0,0,6,2,0,6,3,2,9,2,5,11,
%T A353501 3,5,18,6,4,20,13,8,26,10,17,37,14,16,51,23,24,58,38,32,75,44,52,100,
%U A353501 52,59,143,75,77,159,114,112,203,132,154,266,175
%N A353501 Number of integer partitions of n with all parts and all multiplicities > 2.
%e A353501 The a(n) partitions for selected n (A = 10):
%e A353501 n=9: n=12: n=21: n=24: n=30:
%e A353501 ------------------------------------------------------
%e A353501 (333) (444) (777) (888) (AAA)
%e A353501 (3333) (444333) (6666) (66666)
%e A353501 (3333333) (444444) (555555)
%e A353501 (555333) (666444)
%e A353501 (4443333) (777333)
%e A353501 (33333333) (6663333)
%e A353501 (55533333)
%e A353501 (444333333)
%e A353501 (3333333333)
%t A353501 Table[Length[Select[IntegerPartitions[n],Min@@#>2&&Min@@Length/@Split[#]>2&]],{n,0,30}]
%Y A353501 The version for only parts > 2 is A008483.
%Y A353501 The version for only multiplicities > 2 is A100405.
%Y A353501 The version for parts and multiplicities > 1 is A339222, ranked by A062739.
%Y A353501 For prime parts and multiplicities we have A351982, compositions A353429.
%Y A353501 The version for compositions is A353428 (partial A078012, A353400).
%Y A353501 These partitions are ranked by A353502.
%Y A353501 A000726 counts partitions with all mults <= 2, compositions A128695.
%Y A353501 A004250 counts partitions with some part > 2, compositions A008466.
%Y A353501 A137200 counts compositions with all parts and run-lengths <= 2.
%Y A353501 Cf. A003242, A047966, A055923, A098859, A114901, A325534, A333755, A335464.
%K A353501 nonn
%O A353501 0,13
%A A353501 _Gus Wiseman_, May 16 2022