A135092 Binomial transform of [1, 6, 1, 6, 1, 6, ...].

1, 7, 14, 28, 56, 112, 224, 448, 896, 1792, 3584, 7168, 14336, 28672, 57344, 114688, 229376, 458752, 917504, 1835008, 3670016, 7340032, 14680064, 29360128, 58720256, 117440512, 234881024, 469762048, 939524096, 1879048192, 3758096384, 7516192768, 15032385536

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..3000

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

Formula

a(n) = 7*2^(n-1) for n>0, a(0)=1.

a(n) = Sum_{k=0..n} A097805(n,k)*7^k*(-5)^(n-k). - Philippe Deléham, Nov 19 2007

G.f.: (1+5*x)/(1-2*x). - Bruno Berselli, Sep 20 2011

E.g.f.: (1/2)*(7*exp(2*x) - 5). - G. C. Greubel, Sep 22 2016

a(n) = A125176(n+2) for n >= 1. - Georg Fischer, Nov 02 2018

Example

a(3) = (1, 3, 3, 1) dot (1, 6, 1, 6) = (1 + 18 + 3 + 6) = 28 = 7*2^2.

Mathematica

Join[{1}, NestList[2#&, 7, 50]] (* Harvey P. Dale, Aug 30 2015 *)

Crossrefs

Essentially identical to A005009 and to A125176.

Sequence in context: A196876 A115876 A005009 * A245417 A348111 A332371

Adjacent sequences: A135089 A135090 A135091 * A135093 A135094 A135095

Keyword

nonn,easy

Author

Gary W. Adamson, Nov 18 2007

Extensions

Corrected and extended by Philippe Deléham and N. J. A. Sloane, Dec 15 2007

Status

approved