A165458 a(0)=1, a(1)=4, a(n) = 12*a(n-2) - a(n-1).

1, 4, 8, 40, 56, 424, 248, 4840, -1864, 59944, -82312, 801640, -1789384, 11409064, -32881672, 169790440, -564370504, 2601855784, -9374301832, 40596571240, -153088193224, 640247048104, -2477305366792, 10160269944040, -39887934345544, 161811173674024

Offset: 0

Author

Philippe Deléham, Sep 20 2009

Keywords

• easy
• sign

Comments

a(n)/a(n-1) tends to -4.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,12).

Programs

GAP

a:=[1,4];; for n in [3..27] do a[n]:=12*a[n-2]-a[n-1]; od; a; # Muniru A Asiru, Oct 21 2018

Magma

[(8*3^n-(-4)^n)/7: n in [0..40]]; // G. C. Greubel, Oct 20 2018

Maple

A165458:=n->(8*3^n-(-4)^n)/7: seq(A165458(n), n=0..40); # Wesley Ivan Hurt, May 26 2015

Mathematica

LinearRecurrence[{-1,12},{1,4},30] (* Harvey P. Dale, Dec 26 2015 *)

PARI

vector(40, n, n--; (8*3^n-(-4)^n)/7) \\ G. C. Greubel, Oct 20 2018

Python

for n in range(0, 30): print(int((8*3**n-(-4)**n)/7), end=', ') # Stefano Spezia, Oct 21 2018

Formula

G.f.: (1+5*x)/(1+x-12*x^2).

a(n) = Sum_{k, k=0..n} A112555(n,k)*3^k.

a(n) = (8*3^n-(-4)^n)/7. - Klaus Brockhaus, Sep 26 2009

E.g.f.: (8*exp(3*x) - exp(-4*x))/7. - G. C. Greubel, Oct 20 2018