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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
OFFSET
0,3
COMMENTS
10^(floor((n - 2)/2)) | a(n) for n>=1. - 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).
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
KEYWORD
nonn
AUTHOR
Philippe Deléham, Jan 19 2009
STATUS
approved