A237258 - OEIS

%I #28 Oct 27 2022 18:02:48

%S 1,0,0,1,1,3,4,7,9,16,21,32,43,63,84,122,158,220,293,393,511,685,881,

%T 1156,1485,1925,2445,3147,3952,5019,6323,7924,9862,12336,15259,18900,

%U 23294,28646,35091,42985,52341,63694,77336,93588,112973,136367,163874,196638

%N Number of strict partitions of 2n that include a partition of n.

%C A strict partition is a partition into distinct parts.

%H Fausto A. C. Cariboni, <a href="/A237258/b237258.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = A237194(2n,n).

%e a(5) counts these partitions of 10: [5,4,1], [5,3,2], [4,3,2,1].

%t z = 24; Table[theTotals = Map[{#, Map[Total, Subsets[#]]} &,  Select[IntegerPartitions[2 nn], # == DeleteDuplicates[#] &]]; Length[Map[#[[1]] &, Select[theTotals, Length[Position[#[[2]], nn]] >= 1 &]]], {nn, z}] (* _Peter J. C. Moses_, Feb 04 2014 *)

%Y Cf. A000009, A237194, A235130.

%Y The non-strict version is A002219, ranked by A357976.

%Y These partitions are ranked by A357854.

%Y A000712 counts distinct submultisets of partitions, strict A032302.

%Y A304792 counts subset-sums of partitions, positive A276024, strict A284640.

%Y Cf. A006827, A064914, A108917, A276107, A300061, A357879.

%K nonn

%O 0,6

%A _Clark Kimberling_, Feb 05 2014

%E a(31)-a(47) from _Alois P. Heinz_, Feb 07 2014