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A123362 a(0) = 1, a(1) = 1, a(n) = 6*a(n-1) + 5*a(n-2) for n > 1. 3
1, 1, 11, 71, 481, 3241, 21851, 147311, 993121, 6695281, 45137291, 304300151, 2051487361, 13830424921, 93239986331, 628592042591, 4237752187201, 28569473336161, 192605600952971, 1298480972398631, 8753913839156641 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform is [1, 10, 0, 0, 0, 0, 0, 0, 0, 0, ...]. - Philippe Deléham, Dec 04 2008

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Lucyna Trojnar-Spelina, Iwona Włoch, On Generalized Pell and Pell-Lucas Numbers, Iranian Journal of Science and Technology, Transactions A: Science (2019), 1-7.

Index entries for linear recurrences with constant coefficients, signature (6,5).

FORMULA

a(n) = Sum_{k = 0..n} 5^(n - k)*A122542(n, k).

G.f.: (1 - 5*x)/(1 - 6*x - 5*x^2).

a(n) = (1/2)*(3 + sqrt(14))^n + (1/2)*(3 - sqrt(14))^n - (1/14) * (3 + sqrt(14))^n * sqrt(14) + (1/14) * (3 - sqrt(14))^n * sqrt(14), with n >= 0. - Paolo P. Lava, Jun 25 2008

MATHEMATICA

Table[MatrixPower[{{1, 2}, {5, 5}}, n][[1]][[1]], {n, 0, 44}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)

LinearRecurrence[{6, 5}, {1, 1}, 50] (* G. C. Greubel, Oct 12 2017 *)

PROG

(PARI) x='x+O('x^50); Vec((1-5*x)/(1 - 6*x - 5*x^2)) \\ G. C. Greubel, Oct 12 2017

CROSSREFS

Sequence in context: A164559 A319535 A300541 * A199488 A068847 A139185

Adjacent sequences:  A123359 A123360 A123361 * A123363 A123364 A123365

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Oct 12 2006

STATUS

approved

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Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)