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

0,2

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).

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]

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 *)

Crossrefs

Sequence in context: A287100 A287188 A100347 * A179857 A260078 A163590

Adjacent sequences: A165402 A165403 A165404 * A165406 A165407 A165408

Keyword

sign

Author

Philippe Deléham, Sep 17 2009

Status

approved