A240014 Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 5.

1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 20, 24, 32, 41, 51, 65, 81, 102, 125, 158, 190, 239, 287, 357, 426, 528, 626, 769, 913, 1110, 1314, 1590, 1877, 2255, 2660, 3174, 3738, 4439, 5215, 6162, 7230, 8502, 9954, 11666, 13626, 15911, 18551, 21590, 25118, 29154

Offset

5,5

Comments

With offset 10 number of partitions of n, where the difference between the number of odd parts and the number of even parts is -5.

Links

Alois P. Heinz, Table of n, a(n) for n = 5..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, -5):
seq(a(n), n=5..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, -5];
a /@ Range[5, 80] (* Jean-François Alcover, Dec 10 2020, after Alois P. Heinz *)

Crossrefs

Column k=5 of A240009.

Sequence in context: A266779 A035949 A347445 * A266780 A266781 A035955

Adjacent sequences: A240011 A240012 A240013 * A240015 A240016 A240017

Keyword

nonn

Author

Alois P. Heinz, Mar 30 2014

Status

approved