A103419 Number of compositions of n in which the least part is odd.

1, 1, 4, 6, 14, 28, 59, 117, 239, 484, 980, 1973, 3973, 7989, 16054, 32227, 64653, 129628, 259787, 520440, 1042305, 2086938, 4177680, 8361557, 16733221, 33482909, 66992641, 134028938, 268128902, 536373288, 1072934271, 2146173471, 4292842170, 8586488355

Offset: 1

Author

Vladeta Jovovic, Feb 04 2005

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A103420-A103422, A027187, A027193, A026804, A026805.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, irem(i, 2), add(
      (t-> b(t, min(i, j, `if`(t>0, t, j))))(n-j), j=1..n))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..40);  # Alois P. Heinz, Jul 26 2015

Mathematica

Rest[ CoefficientList[ Series[ Expand[ Sum[(1 - x)^2*x^(2n - 1)/((1 - x - x^(2n))*(1 - x - x^(2n - 1))), {n, 35}]], {x, 0, 35}], x]] (* Robert G. Wilson v, Feb 05 2005 *)

Formula

G.f.: Sum((1-x)^2*x^(2*n-1)/((1-x-x^(2*n))*(1-x-x^(2*n-1))), n=1..infinity).

G.f.: Sum(x^k/((1-x)^k*(1+x^k)),k=1..infinity). - Vladeta Jovovic, Mar 02 2008

a(n) ~ 2^(n-1). - Vaclav Kotesovec, May 01 2014

Extensions

More terms from Robert G. Wilson v, Feb 05 2005