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
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..1000
Programs
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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