A103421 Number of compositions of n in which the greatest part is odd.

1, 1, 2, 3, 7, 14, 30, 62, 129, 263, 534, 1076, 2160, 4318, 8612, 17145, 34097, 67764, 134638, 267506, 531606, 1056812, 2101854, 4182462, 8327263, 16588973, 33066080, 65945522, 131588128, 262702054, 524699094, 1048433468, 2095744336

Offset

1,3

Links

Table of n, a(n) for n=1..33.

Formula

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).

a(n) + A103422(n) = 2^(n-1). - R. J. Mathar, Mar 24 2018

Mathematica

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 *)

Crossrefs

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

Sequence in context: A192570 A019595 A112884 * A205484 A151530 A180752

Adjacent sequences: A103418 A103419 A103420 * A103422 A103423 A103424

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 04 2005

Extensions

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

Status

approved