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
Examples
a(3) = (1, 3, 3, 1) dot (1, 6, 1, 6) = (1 + 18 + 3 + 6) = 28 = 7*2^2.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..3000
- Index entries for linear recurrences with constant coefficients, signature (2).
Programs
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Mathematica
Join[{1},NestList[2#&,7,50]] (* Harvey P. Dale, Aug 30 2015 *)
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
Extensions
Corrected and extended by Philippe Deléham and N. J. A. Sloane, Dec 15 2007