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A240012
Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 3.
2
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
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 * A375134 A295261 A293627
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 30 2014
STATUS
approved