A080925 Binomial transform of Jacobsthal gap sequence (A080924).

0, 1, 5, 13, 41, 121, 365, 1093, 3281, 9841, 29525, 88573, 265721, 797161, 2391485, 7174453, 21523361, 64570081, 193710245, 581130733, 1743392201, 5230176601, 15690529805, 47071589413, 141214768241, 423644304721, 1270932914165

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (2,3).

Formula

a(n)=Sum{k=1..n, Binomial(n, 2k-2)2^(2k-2)}

a(n)=(3^n-2*0^n+(-1)^n)/2; G.f.: x(1+3x)/((1+x)(1-3x)); E.g.f.: (exp(3x)-2exp(0)+exp(-x))/2. - Paul Barry, May 19 2003

Mathematica

CoefficientList[Series[x (1 + 3 x) / ((1 + x) (1 - 3 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 05 2013 *)

Crossrefs

Cf. A046717, A080926.

Sequence in context: A287017 A229747 A182300 * A164907 A046717 A352916

Adjacent sequences: A080922 A080923 A080924 * A080926 A080927 A080928

Keyword

easy,nonn

Author

Paul Barry, Feb 26 2003

Status

approved