A097068 a(n)=Sum(C(n,2k+1)5^k 3^(2k+1) 7^(n-2k-1), k=0,..,Floor[(n-1)/2]).

0, 3, 42, 576, 7896, 108240, 1483776, 20339904, 278823552, 3822170112, 52395087360, 718242542592, 9845815246848, 134968443285504, 1850174945009664, 25362575456993280, 347675356617867264

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (14, -4).

Formula

a(n)=2^(n-1)F(4n), where F(n) are Fibonacci numbers A000045

a(n)= 14*a(n-1) -4*a(n-2). G.f.: 3*x/(1-14*x+4*x^2). [From R. J. Mathar, Feb 06 2010]

Mathematica

Table[Sum[Binomial[n, 2k + 1]5^k 3^(2k + 1)7^(n-2k-1), {k, 0, Floor[(n - 1)/2]}], {n, 0, 25}]

Crossrefs

Sequence in context: A003770 A173936 A219619 * A269046 A092470 A355796

Adjacent sequences: A097065 A097066 A097067 * A097069 A097070 A097071

Keyword

easy,nonn

Author

Mario Catalani (mario.catalani(AT)unito.it), Jul 22 2004

Status

approved