A103421 - OEIS

%I #11 Mar 24 2018 17:19:59

%S 1,1,2,3,7,14,30,62,129,263,534,1076,2160,4318,8612,17145,34097,67764,

%T 134638,267506,531606,1056812,2101854,4182462,8327263,16588973,

%U 33066080,65945522,131588128,262702054,524699094,1048433468,2095744336

%N Number of compositions of n in which the greatest part is odd.

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

%F a(n) + A103422(n) = 2^(n-1). - _R. J. Mathar_, Mar 24 2018

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

%Y Cf. A103419, A103420, A103422, A027187, A027193, A026804, A026805.

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Feb 04 2005

%E More terms from _Robert G. Wilson v_, Feb 05 2005