A240012 Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 3.

1, 0, 1, 1, 2, 2, 4, 4, 6, 8, 10, 14, 17, 23, 27, 38, 43, 59, 69, 91, 106, 139, 162, 207, 245, 306, 364, 449, 534, 650, 778, 934, 1117, 1334, 1592, 1887, 2251, 2652, 3155, 3705, 4391, 5139, 6075, 7086, 8347, 9720, 11406, 13252, 15505, 17978, 20965, 24272

Offset

3,5

Comments

With offset 6 number of partitions of n, where the difference between the number of odd parts and the number of even parts is -3.

Links

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Maple

b:= proc(n, i, t) option remember; `if`(abs(t)>n, 0,
      `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, t)+
      `if`(i>n, 0, b(n-i, i, t+(2*irem(i, 2)-1))))))
    end:
a:= n-> b(n$2, -3):
seq(a(n), n=3..80);

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[Abs[t] > n, 0, If[n == 0, 1, If[i < 1, 0, b[n, i - 1, t] + If[i > n, 0, b[n - i, i, t + 2 Mod[i, 2] - 1]]]]];
a[n_] := b[n, n, -3];
a /@ Range[3, 80] (* Jean-François Alcover, Dec 10 2020, after Alois P. Heinz *)

Crossrefs

Column k=3 of A240009.

Sequence in context: A087135 A227135 A162417 * A295261 A293627 A264393

Adjacent sequences: A240009 A240010 A240011 * A240013 A240014 A240015

Keyword

nonn

Author

Alois P. Heinz, Mar 30 2014

Status

approved