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A103419
Number of compositions of n in which the least part is odd.
4
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
1,3
LINKS
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
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 *)
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Feb 04 2005
EXTENSIONS
More terms from Robert G. Wilson v, Feb 05 2005
STATUS
approved