A119968 Binomial transform of Fredholm-Rueppel sequence.

1, 2, 3, 5, 9, 16, 27, 44, 73, 130, 251, 507, 1025, 2016, 3811, 6907, 12033, 20282, 33475, 55253, 94185, 171896, 342651, 737266, 1655657, 3751786, 8386587, 18274843, 38629505, 79123224, 157157411, 303174298, 569093601, 1041436386

Offset

0,2

Comments

Binomial transform of A036987.

Number of compositions of n such that number of parts is of the form 2^m, m>=0 (offset 1). - Vladeta Jovovic, Jun 27 2007

Links

Table of n, a(n) for n=0..33.

Formula

G.f.: (1/(1-x))*sum{k>=0, (x/(1-x))^(2^k-1)}; a(n)=sum{k=0..n, C(n,2^k-1)}; a(n)=sum{k=0..n, C(n,k)*mod(C(k),2)};

Mathematica

Table[Sum[Binomial[n, 2^k-1], {k, 0, n}], {n, 0, 40}] (* Harvey P. Dale, Aug 18 2012 *)

Crossrefs

Sequence in context: A269153 A232866 A011826 * A291311 A017914 A137402

Adjacent sequences: A119965 A119966 A119967 * A119969 A119970 A119971

Keyword

easy,nonn

Author

Paul Barry, Jun 01 2006

Status

approved