A238742 Number of partitions p of 2n+1 such that n - (number of parts of p) is a part of p.

0, 0, 1, 5, 13, 31, 59, 109, 180, 301, 461, 712, 1051, 1547, 2200, 3138, 4349, 6036, 8211, 11146, 14901, 19908, 26232, 34513, 44953, 58412, 75244, 96752, 123448, 157201, 198931, 251155

Offset: 1

Author

Clark Kimberling, Mar 04 2014

Keywords

• nonn
• easy

Examples

			a(4) counts these partitions of 9:  72, 711, 621, 531, 441.
		

Links

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

Crossrefs

Cf. A238640, A238741.

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_] := 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+1, u, n-u], {u, n-1}]; Array[a, 100] (* Giovanni Resta, Mar 12 2014 *)