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A171510 Generalized Lucas numbers: a(n) = 10*a(n-1) + a(n-2), with a(1)=2 and a(2)=1. 1
2, 1, 12, 121, 1222, 12341, 124632, 1258661, 12711242, 128371081, 1296422052, 13092591601, 132222338062, 1335315972221, 13485382060272, 136189136574941, 1375376747809682, 13889956614671761, 140274942894527292, 1416639385559944681, 14306668798493974102 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Colin Barker, Table of n, a(n) for n = 1..997

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

FORMULA

a(n) = (5+sqrt(26))^(n-1)-9/52*(5+sqrt(26))^(n-1)*sqrt(26)+(5-sqrt(26))^(n-1)+9/52*sqrt(26)*(5 -sqrt(26))^(n-1), with n>=1. - Paolo P. Lava, Dec 14 2009

G.f.: x*(19*x-2) / (x^2+10*x-1). - Colin Barker, Oct 02 2015

MATHEMATICA

RecurrenceTable[{a[n] == 10 a[n - 1] + a[n - 2], a[1] == 2, a[2] == 1}, a, {n, 1, 21}] (* or *) LinearRecurrence[{10, 1}, {2, 1}, 21] (* Michael De Vlieger, Oct 02 2015 *)

PROG

(PARI) Vec(x*(19*x-2)/(x^2+10*x-1) + O(x^40)) \\ Colin Barker, Oct 02 2015

CROSSREFS

Cf. A015456, A065941.

Sequence in context: A009483 A181867 A231611 * A106750 A258821 A124916

Adjacent sequences:  A171507 A171508 A171509 * A171511 A171512 A171513

KEYWORD

nonn,easy

AUTHOR

Mark Dols, Dec 10 2009

STATUS

approved

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Last modified September 19 21:42 EDT 2020. Contains 337184 sequences. (Running on oeis4.)