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A165511 a(0)=1, a(1)=10, a(n) = 90*a(n-2) - a(n-1). 2
1, 10, 80, 820, 6380, 67420, 506780, 5561020, 40049180, 460442620, 3143983580, 38295852220, 244662669980, 3201964029820, 18817676268380, 269359086415420, 1424231777738780, 22818085999649020, 105362773996841180 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 15 22:06 EDT 2021. Contains 345053 sequences. (Running on oeis4.)