The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #6 Dec 10 2025 16:32:03
%S 0,1,0,1,0,2,0,2,1,3,1,4,2,5,4,7,6,9,8,13,12,16,17,23,24,29,32,40,43,
%T 52,57,69,76,88,100,117,129,148,167,193,215,245,274,313,349,394,442,
%U 500,557,625,698,784,873,977,1087,1216,1349,1502,1669,1858
%N Number of strict integer partitions of n > 0 such that the least part and the greatest part are both even.
%e The a(10) = 3 through a(16) = 7 strict partitions:
%e (10) (6,3,2) (12) (6,5,2) (14) (6,5,4) (16)
%e (6,4) (8,4) (8,3,2) (8,6) (8,5,2) (10,6)
%e (8,2) (10,2) (10,4) (10,3,2) (12,4)
%e (6,4,2) (12,2) (6,4,3,2) (14,2)
%e (8,4,2) (8,6,2)
%e (10,4,2)
%e (6,5,3,2)
%t Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&EvenQ[First[#]]&&EvenQ[Last[#]]&]],{n,30}]
%Y For odd least part we have A026832, non-strict A026804, ranks A340932.
%Y For even least part we have A026833, non-strict A026805, ranks A340933.
%Y For odd greatest part we have A026837, non-strict A027193, ranks A244991.
%Y For even greatest part we have A067661, non-strict A027187, ranks A244990.
%Y The non-strict version is A325346, ranks A391232.
%Y For sum instead of product we have A390746, non-strict A390092, ranks A390988.
%Y For both parts odd we have A391228, non-strict A325338, ranks A390093.
%Y A000041 counts integer partitions, strict A000009.
%Y A257991 counts odd prime indices, even A257992.
%Y Cf. A000700, A005843, A035457, A058696, A066207, A067659, A160786, A300061, A390430, A391227, A391231.
%K nonn
%O 1,6
%A _Gus Wiseman_, Dec 10 2025