A165405 a(0)=1, a(1)=3,a(n)=6*a(n-2)-a(n-1).

1, 3, 3, 15, 3, 87, -69, 591, -1005, 4551, -10581, 37887, -101373, 328695, -936933, 2909103, -8530701, 25985319, -77169525, 233081439, -696098589, 2094587223, -6271178757, 18838702095, -56465774637, 169497987207, -508292635029

Offset: 0

Author

Philippe Deléham, Sep 17 2009

Keywords

• sign

Comments

a(n)/a(n-1) tends to -3.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,6).

Programs

Mathematica

nxt[{a_,b_}]:={b,6a-b}; NestList[nxt,{1,3},30][[;;,1]] (* or *) LinearRecurrence[{-1,6},{1,3},30] (* Harvey P. Dale, May 24 2024 *)

Formula

G.f.: (1+4x)/(1+x-6x^2). a(n)= Sum_{k, 0<=k<=n}A112555(n,k)*2^k.

a(n) = (6*2^n-(-3)^n)/5. [From Klaus Brockhaus, Sep 26 2009]