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A238607 Number of partitions p of 2n such that n - (number of parts of p) is a part of p. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A238641, A238742.

Sequence in context: A102651 A102652 A279626 * A143270 A037338 A136486

Adjacent sequences:  A238604 A238605 A238606 * A238608 A238609 A238610

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 04 2014

EXTENSIONS

More terms from Alois P. Heinz, Mar 04 2014

STATUS

approved

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Last modified May 15 06:18 EDT 2021. Contains 343909 sequences. (Running on oeis4.)