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A238742
Number of partitions p of 2n+1 such that n - (number of parts of p) is a part of p.
3
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
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
Sequence in context: A332368 A203246 A106985 * A023261 A165888 A021007
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 04 2014
STATUS
approved