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A240013 Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 4. 2
1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 11, 14, 19, 24, 30, 40, 48, 63, 76, 98, 117, 151, 178, 227, 269, 337, 399, 496, 586, 720, 854, 1036, 1228, 1481, 1752, 2096, 2480, 2946, 3481, 4115, 4850, 5707, 6717, 7868, 9237, 10789, 12632, 14707, 17181, 19947, 23243, 26925 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,5

COMMENTS

With offset 8 number of partitions of n, where the difference between the number of odd parts and the number of even parts is -4.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..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, -4):

seq(a(n), n=4..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, -4];

a /@ Range[4, 80] (* Jean-Fran├žois Alcover, Dec 10 2020, after Alois P. Heinz *)

CROSSREFS

Column k=4 of A240009.

Sequence in context: A339404 A035944 A227134 * A050366 A332753 A027591

Adjacent sequences:  A240010 A240011 A240012 * A240014 A240015 A240016

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 30 2014

STATUS

approved

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Last modified January 26 14:30 EST 2021. Contains 340439 sequences. (Running on oeis4.)