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A165312 a(0)=1, a(1)=5, a(n)=11*a(n-1)-25*a(n-2) for n>1. 3
1, 5, 30, 205, 1505, 11430, 88105, 683405, 5314830, 41378005, 322287305, 2510710230, 19560629905, 152399173205, 1187375157630, 9251147403805, 72078242501105, 561581982417030, 4375445744059705, 34090353624231005 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)/a(n-1) tends to (11+sqrt(21))/2 = 7.79128784...

For n>=2, a(n) equals 5^n times the permanent of the (2n-2)X(2n-2) tridiagonal matrix with 1/sqrt(5)'s along the main diagonal, and 1's along the superdiagonal and the subdiagonal. [From John M. Campbell, Jul 08 2011]

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..1119

Index entries for linear recurrences with constant coefficients, signature (11,-25).

FORMULA

G.f.: (1-6x)/(1-11x+25x^2). a(n)=Sum_{k, 0<=k<=n}A165253(n,k)*5^(n-k).

a(n) = ((21-sqrt(21))*(11+sqrt(21))^n+(21+sqrt(21))*(11-sqrt(21))^n )/(42*2^n). [From Klaus Brockhaus, Sep 26 2009]

MATHEMATICA

LinearRecurrence[{11, -25}, {1, 5}, 30] (* Harvey P. Dale, Oct 02 2016 *)

CROSSREFS

Sequence in context: A234422 A091927 A253076 * A082301 A144180 A222050

Adjacent sequences:  A165309 A165310 A165311 * A165313 A165314 A165315

KEYWORD

nonn

AUTHOR

Philippe Deléham, Sep 14 2009

STATUS

approved

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Last modified January 21 11:19 EST 2019. Contains 319353 sequences. (Running on oeis4.)