A155199 a(n) = 10*a(n-1) + a(n-2), n > 2 ; a(0) = 1, a(1) = 9, a(2) = 90.

1, 9, 90, 909, 9180, 92709, 936270, 9455409, 95490360, 964359009, 9739080450, 98355163509, 993290715540, 10031262318909, 101305913904630, 1023090401365209, 10332209927556720, 104345189676932409, 1053784106696880810, 10642186256645740509, 107475646673154285900

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (10,1).

Formula

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

a(n) = Sum_{k=0..n} A155161(n,k)*9^k. - Philippe Deléham, Feb 08 2012

E.g.f.: 1 + 9*exp(5*x)*sinh(sqrt(26)*x)/sqrt(26). - Stefano Spezia, Mar 01 2023

Mathematica

LinearRecurrence[{10, 1}, {1, 9, 90}, 20] (* Harvey P. Dale, Dec 20 2022 *)

Crossrefs

Cf. A001019, A155161.

Sequence in context: A299872 A173480 A052268 * A147841 A036258 A098399

Adjacent sequences: A155196 A155197 A155198 * A155200 A155201 A155202

Keyword

nonn,easy

Author

Philippe Deléham, Jan 21 2009

Status

approved