A165491 a(0)=1, a(1)=6, a(n) = 30*a(n-2) - a(n-1).

1, 6, 24, 156, 564, 4116, 12804, 110676, 273444, 3046836, 5156484, 86248596, 68445924, 2519011956, -465634236, 76035992916, -90005019996, 2371084807476, -5071235407356, 76203779631636, -228340841852316, 2514454230801396

Offset: 0

Author

Philippe Deléham, Sep 21 2009

Keywords

• easy
• sign

Comments

a(n)/a(n-1) tends to -6.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1, 30).

Programs

GAP

a:=[1,6];; for n in [3..22] do a[n]:=30*a[n-2]-a[n-1]; od; a; # Muniru A Asiru, Oct 21 2018

Magma

[(12*5^n-(-6)^n)/11: n in [0..30]]; // G. C. Greubel, Oct 20 2018

Maple

seq(coeff(series((1+7*x)/(1+x-30*x^2),x,n+1), x, n), n = 0 .. 22); # Muniru A Asiru, Oct 21 2018

Mathematica

LinearRecurrence[{-1,30},{1,6},30] (* Harvey P. Dale, May 04 2012 *)

PARI

vector(30, n, n--; (12*5^n-(-6)^n)/11) \\ G. C. Greubel, Oct 20 2018

Formula

G.f.: (1+7*x)/(1+x-30*x^2).

a(n) = Sum_{k=0..n} A112555(n,k)*5^k.

a(n) = (12*5^n-(-6)^n)/11. - Klaus Brockhaus, Sep 26 2009

E.g.f.: (12*exp(5*x) - exp(-6*x))/11. - G. C. Greubel, Oct 20 2018