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

Author

Paul Barry, Jun 01 2006

Keywords

• easy
• nonn

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

Programs

Mathematica

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

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)};