A096967 Bisection of A096441.

0, 2, 4, 7, 11, 17, 26, 37, 54, 76, 106, 145, 199, 266, 357, 472, 621, 809, 1053, 1354, 1740, 2218, 2818, 3559, 4485, 5616, 7018, 8728, 10826, 13373, 16484, 20236, 24793, 30275, 36886, 44810, 54329, 65683, 79265, 95419, 114650, 137447, 164496, 196445, 234221

Offset: 0

Author

N. J. A. Sloane, Aug 20 2004

Keywords

• nonn

Comments

Number of partitions of 2n such that either all parts are odd or all parts are even, n >= 1. - Omar E. Pol, Aug 16 2013

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A096441, A078408.

Programs

Maple

b:= proc(n, i) option remember; `if`(i>n, 0,
      `if`(irem(n, i)=0, 1, 0)+add(`if`(irem(j, 2)=0,
       b(n-i*j, i+1), 0), j=0..n/i))
    end:
a:= n-> b(2*n, 1):
seq(a(n), n=0..60);  # Alois P. Heinz, Mar 26 2014

Mathematica

b[n_, i_] := b[n, i] = If[i>n, 0, If[Mod[n, i]==0, 1, 0] + Sum[If[Mod[j, 2] ==0, b[n-i*j, i+1], 0], {j, 0, n/i}]]; a[n_] := b[2*n, 1]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Jan 17 2016, after Alois P. Heinz *)