A171967 Number of partitions of n with distinct numbers of odd and even parts.

0, 1, 2, 2, 5, 5, 10, 12, 20, 25, 37, 49, 68, 90, 119, 158, 206, 269, 344, 446, 565, 722, 908, 1148, 1435, 1795, 2229, 2765, 3416, 4204, 5164, 6315, 7717, 9380, 11406, 13793, 16692, 20093, 24203, 29012, 34799, 41552, 49636, 59059, 70279, 83341, 98822

Offset

0,3

Comments

a(n) = A000041(n) - A045931(n) = A108949(n) + A108950(n).

a(n) = Sum_{k<>0} A240009(n,k). - Alois P. Heinz, Mar 30 2014

Links

Alois P. Heinz, Table of n, a(n) for n = 0..3500

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+(2*irem(i, 2)-1)))))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..80);  # Alois P. Heinz, Mar 30 2014

Mathematica

$RecursionLimit = 1000; 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+(2*Mod[i, 2]-1)]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Jun 30 2015, after Alois P. Heinz *)

Crossrefs

Cf. A130780, A171966.

Sequence in context: A306320 A347449 A325347 * A079964 A184321 A103891

Adjacent sequences: A171964 A171965 A171966 * A171968 A171969 A171970

Keyword

nonn

Author

Reinhard Zumkeller, Jan 21 2010

Status

approved