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A155017 a(n) = 10*a(n-1) + 90*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=19 . 2
1, 1, 19, 280, 4510, 70300, 1108900, 17416000, 273961000, 4307050000, 67726990000, 1064904400000, 16744473100000, 263286127000000, 4139863849000000, 65094389920000000, 1023531645610000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

10^(floor((n - 2)/2)) | a(n) for n>=1. - G. C. Greubel, Dec 30 2017

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..825

Index entries for linear recurrences with constant coefficients, signature (10, 90).

FORMULA

G.f.: (1-9*x-81*x^2)/(1-10*x-90*x^2).

a(n+1) = Sum_{k=0..n} A154929(n,k)*9^(n-k).

a(n) = (7/115)*sqrt(115)*{[5+sqrt(115)]^(n-1)-[5-sqrt(115)]^(n-1)}+(1/2)*{[5-sqrt(115)]^(n-1)+[5+sqrt(115)]^(n-1)}+(9/10)*[C(2*n,n) mod 2], with n>=0. - Paolo P. Lava, Jan 26 2009

MATHEMATICA

Join[{1}, LinearRecurrence[{10, 90}, {1, 19}, 20]] (* Harvey P. Dale, Oct 10 2012 *)

CoefficientList[Series[(1 - 9*x - 81*x^2)/(1 - 10*x - 90*x^2), {x, 0, 50}], x] (* G. C. Greubel, Dec 30 2017 *)

PROG

(PARI) x='x+O('x^30); Vec((1-9*x-81*x^2)/(1-10*x-90*x^2)) \\ G. C. Greubel, Dec 30 2017

(Magma) I:=[1, 1, 19]; [1] cat [n le 2 select I[n] else 10*Self(n-1) + 90*Self(n-2): n in [1..30]]; // G. C. Greubel, Dec 30 2017

CROSSREFS

Sequence in context: A322053 A328916 A081045 * A199245 A152591 A051562

Adjacent sequences: A155014 A155015 A155016 * A155018 A155019 A155020

KEYWORD

nonn

AUTHOR

Philippe Deléham, Jan 19 2009

STATUS

approved

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Last modified December 3 23:05 EST 2022. Contains 358543 sequences. (Running on oeis4.)