A165511 a(0)=1, a(1)=10, a(n) = 90*a(n-2) - a(n-1).

1, 10, 80, 820, 6380, 67420, 506780, 5561020, 40049180, 460442620, 3143983580, 38295852220, 244662669980, 3201964029820, 18817676268380, 269359086415420, 1424231777738780, 22818085999649020, 105362773996841180

Offset

0,2

Comments

a(n)/a(n-1) tends to -10.

First entry < 0: a(30) = -8009307078719785774426912420.

Links

G. C. Greubel, Table of n, a(n) for n = 0..998 (terms 0..100 from Franklin T. Adams-Watters)

Index entries for linear recurrences with constant coefficients, signature (-1, 90).

Formula

G.f.: (1+11*x)/(1+x-90*x^2).

a(n) = Sum_{k=0..n} A112555(n,k)*9^k.

a(n) = (20*9^n-(-10)^n)/19. - Klaus Brockhaus, Sep 26 2009

E.g.f.: (20*exp(9*x) - exp(-10*x))/19. - G. C. Greubel, Oct 21 2018

Mathematica

LinearRecurrence[{-1, 90}, {1, 10}, 20] (* or *) CoefficientList[Series[ (1+11x)/(1+x-90x^2), {x, 0, 20}], x]  (* Harvey P. Dale, Apr 30 2011 *)

Prog

(PARI) vector(50, n, n--; (20*9^n-(-10)^n)/19) \\ G. C. Greubel, Oct 21 2018
(Magma) [(20*9^n-(-10)^n)/19: n in [0..50]]; // G. C. Greubel, Oct 21 2018

Crossrefs

Sequence in context: A037692 A126531 A200162 * A165750 A297869 A138425

Adjacent sequences: A165508 A165509 A165510 * A165512 A165513 A165514

Keyword

sign

Author

Philippe Deléham, Sep 21 2009

Status

approved