A171966 Number of partitions of n having no more odd than even parts.

1, 0, 1, 1, 2, 3, 4, 6, 8, 12, 15, 21, 28, 37, 49, 63, 83, 105, 138, 171, 223, 275, 353, 433, 551, 673, 846, 1031, 1282, 1558, 1922, 2327, 2848, 3440, 4179, 5032, 6078, 7293, 8763, 10482, 12534, 14943, 17797, 21146, 25090, 29719, 35138, 41493, 48908, 57578

Offset

0,5

Comments

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

a(n) = Sum_{k=-floor(n/2)+(n mod 2)..0} A240009(n,k). - Alois P. Heinz, Mar 30 2014

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..8000 (terms 0..1000 from Alois P. Heinz)

Formula

From Vaclav Kotesovec, Feb 20 2026: (Start)

a(n) ~ (2 - sqrt(2)) * exp(Pi*sqrt(2*n/3)) / (8*n*sqrt(3)).

a(n) ~ A000041(n) * (1 - 1/sqrt(2)). (End)

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, A171967, A240009.

Sequence in context: A081029 A396075 A300787 * A034893 A187448 A321266

Adjacent sequences: A171963 A171964 A171965 * A171967 A171968 A171969

Keyword

nonn

Author

Reinhard Zumkeller, Jan 21 2010

Status

approved