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 A325269 #17 Feb 02 2023 05:08:10
%S A325269 0,0,0,2,3,6,9,14,20,29,40,55,75,100,133,175,229,296,383,489,625,791,
%T A325269 1000,1254,1573,1957,2434,3009,3716,4564,5602,6841,8347,10142,12308,
%U A325269 14882,17975,21636,26013,31184,37336,44582,53172,63260,75173,89133,105556
%N A325269 Number of integer partitions of n with 2 distinct parts or at least 3 parts.
%C A325269 The Heinz numbers of these partitions are given by A080257.
%C A325269 Partitions with 2 distinct parts are in A002133(n). Partitions with at least 3 parts are in A004250(n). Some partitions are in both subsets, so A002133(n)+A004250(n) >= a(n). - _R. J. Mathar_, Dec 13 2022
%F A325269 conjecture: a(n) = A000041(n) - A000034(n-1), n>0. - _R. J. Mathar_, Dec 13 2022
%e A325269 The a(1) = 1 through a(8) = 20 partitions:
%e A325269 (21) (31) (32) (42) (43) (53)
%e A325269 (111) (211) (41) (51) (52) (62)
%e A325269 (1111) (221) (222) (61) (71)
%e A325269 (311) (321) (322) (332)
%e A325269 (2111) (411) (331) (422)
%e A325269 (11111) (2211) (421) (431)
%e A325269 (3111) (511) (521)
%e A325269 (21111) (2221) (611)
%e A325269 (111111) (3211) (2222)
%e A325269 (4111) (3221)
%e A325269 (22111) (3311)
%e A325269 (31111) (4211)
%e A325269 (211111) (5111)
%e A325269 (1111111) (22211)
%e A325269 (32111)
%e A325269 (41111)
%e A325269 (221111)
%e A325269 (311111)
%e A325269 (2111111)
%e A325269 (11111111)
%p A325269 A325269 := proc(n)
%p A325269 local a,p,s ;
%p A325269 a := 0 ;
%p A325269 for p in combinat[partition](n) do
%p A325269 s := convert(p,set) ;
%p A325269 if nops(p) >= 3 or nops(s) = 2 then
%p A325269 a := a+1 ;
%p A325269 end if;
%p A325269 end do:
%p A325269 a ;
%p A325269 end proc:
%p A325269 seq(A325269(n),n=0..40) ; # _R. J. Mathar_, Dec 13 2022
%t A325269 Table[Length[Select[IntegerPartitions[n],Length[Union[#]]==2||Length[#]>2&]],{n,0,30}]
%Y A325269 Cf. A001221, A001222, A001358, A001399, A007774, A008284, A060687, A080257, A090858, A116608, A325244.
%Y A325269 Cf. A000041, A002133, A004250.
%K A325269 nonn
%O A325269 0,4
%A A325269 _Gus Wiseman_, Apr 18 2019