A238607 Number of partitions p of 2n such that n - (number of parts of p) is a part of p.

0, 0, 1, 4, 12, 24, 49, 85, 147, 232, 374, 558, 843, 1223, 1774, 2493, 3519, 4835, 6659, 8999, 12144, 16152, 21479, 28186, 36945, 47959, 62126, 79805, 102352, 130286, 165546, 209070, 263461, 330266, 413207, 514486, 639342, 791261, 977301, 1202636, 1477172

Offset: 1

Author

Clark Kimberling, Mar 04 2014

Keywords

• nonn
• easy

Examples

			a(4) counts these partitions of 8:  62, 611, 521, 431.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A238641, A238742.

Programs

Mathematica

z = 30; g[n_] := IntegerPartitions[n]; m[p_, t_] := MemberQ[p, t];
Table[Count[g[2 n], p_ /; m[p, n - Length[p]]], {n, z}] (*A238607*)
Table[Count[g[2 n - 1], p_ /; m[p, n - Length[p]]], {n, z}] (*A238641*)
Table[Count[g[2 n + 1], p_ /; m[p, n - Length[p]]], {n, z}] (*A238742*)
p[n_, k_] := p[n, k] = If[k == 1 || n == k, 1, If[k > n, 0, p[n-1, k-1] + p[n-k, k]]]; q[n_, k_, e_] := If[n-e < k-1, 0, If[k == 1, If[n == e, 1, 0], p[n-e, k-1]]]; a[n_] := Sum[q[2*n, u, n-u], {u, n-1}]; Array[a, 100] (* Giovanni Resta, Mar 07 2014 *)

Extensions

More terms from Alois P. Heinz, Mar 04 2014