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

1,4

Links

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

Example

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

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 *)

Crossrefs

Cf. A238640, A238741.

Sequence in context: A332368 A203246 A106985 * A023261 A165888 A021007

Adjacent sequences: A238739 A238740 A238741 * A238743 A238744 A238745

Keyword

nonn,easy

Author

Clark Kimberling, Mar 04 2014

Status

approved