A155017 a(n) = 10*a(n-1) + 90*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=19 .

1, 1, 19, 280, 4510, 70300, 1108900, 17416000, 273961000, 4307050000, 67726990000, 1064904400000, 16744473100000, 263286127000000, 4139863849000000, 65094389920000000, 1023531645610000000

Offset: 0

Author

Philippe Deléham, Jan 19 2009

Keywords

• nonn

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).

Programs

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

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 *)

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

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).