A239004 Number of partitions of n having twice as many even parts as odd.

1, 0, 0, 0, 0, 1, 0, 2, 0, 4, 1, 6, 2, 9, 5, 13, 9, 18, 17, 25, 28, 35, 46, 49, 70, 70, 107, 101, 156, 145, 227, 210, 321, 303, 453, 436, 628, 622, 868, 884, 1187, 1243, 1619, 1738, 2192, 2410, 2960, 3317, 3977, 4532, 5331, 6154, 7117, 8298, 9477, 11129

Offset

0,8

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Example

a(11) counts these 6 partitions:  821, 722, 641, 632, 542, 443.

Maple

b:= proc(n, i, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(i<1, 0, b(n, i-1, t)+
      `if`(i>n, 0, b(n-i, i, t+`if`(irem(i, 2)=1, 2, -1)))))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..60);  # Alois P. Heinz, Mar 14 2014

Mathematica

p[n_] := p[n] = Select[IntegerPartitions[n], 2*Count[#, _?OddQ] == Count[#, _?EvenQ] &];  Table[p[n], {n, 0, 16}] (* shows partitions *)
TableForm[t] (* partitions, vertical format *)
Table[Length[p[n]], {n, 0, 60}] (* A239004 *)
(* Peter J. C. Moses, Mar 10 2014 *)
b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t==0, 1, 0], If[i<1, 0, b[n, i-1, t] + If[i>n, 0, b[n-i, i, t + If[Mod[i, 2] == 1, 2, -1]]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Sep 01 2016, after Alois P. Heinz *)

Crossrefs

Cf. A239258.

Sequence in context: A289144 A350576 A008797 * A168036 A371499 A217930

Adjacent sequences: A239001 A239002 A239003 * A239005 A239006 A239007

Keyword

nonn,easy

Author

Clark Kimberling, Mar 13 2014

Status

approved