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A239004 Number of partitions of n having twice as many even parts as odd. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Sep 01 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A239258.

Sequence in context: A056737 A289144 A008797 * A168036 A217930 A305371

Adjacent sequences:  A239001 A239002 A239003 * A239005 A239006 A239007

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 13 2014

STATUS

approved

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Last modified July 19 22:14 EDT 2019. Contains 325168 sequences. (Running on oeis4.)