A165510 a(0)=1, a(1)=9, a(n) = 72*a(n-2) - a(n-1).

1, 9, 63, 585, 3951, 38169, 246303, 2501865, 15231951, 164902329, 931798143, 10941169545, 56148296751, 731615910489, 3311061455583, 49365284099625, 189031140702351, 3365269314470649, 10244972816098623, 232054417825788105

Offset: 0

Author

Philippe Deléham, Sep 21 2009

Keywords

• sign

Comments

a(n)/a(n-1) tends to -9.

First term < 0: a(27) = -60053864762402471338497.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1, 72).

Programs

Magma

[(18*8^n-(-9)^n)/17: n in [0..30]]; // G. C. Greubel, Oct 21 2018

Mathematica

LinearRecurrence[{-1,72},{1,9},30] (* Harvey P. Dale, Oct 15 2012 *)

PARI

vector(30, n, n--; (18*8^n-(-9)^n)/17) \\ G. C. Greubel, Oct 21 2018

Formula

G.f.: (1+10*x)/(1+x-72*x^2).

a(n) = Sum_{k=0..n} A112555(n,k)*8^k.

a(n) = (18*8^n-(-9)^n)/17. - Klaus Brockhaus, Sep 26 2009

E.g.f.: (18*exp(8*x) - exp(-9*x))/17. - G. C. Greubel, Oct 21 2018