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A159289 a(n+1) = 5*a(n) - 2*a(n-1). 2
5, 21, 95, 433, 1975, 9009, 41095, 187457, 855095, 3900561, 17792615, 81161953, 370224535, 1688798769, 7703544775, 35140126337, 160293542135, 731187458001, 3335350205735, 15214376112673, 69401180151895, 316577148534129 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (5, -2).

FORMULA

From R. J. Mathar, Apr 10 2009: (Start)

G.f.: -(-5+4*x)/(1-5*x+2*x^2).

a(n) = 5*A107839(n) - 4*A107839(n-1). (End)

a(n) = (5/2)*((5/2 + (1/2)*sqrt(17))^n + (5/2 - (1/2)*sqrt(17))^n) + (1/2)*sqrt(17)*((5/2 + (1/2)*sqrt(17))^n - (5/2 - (1/2)*sqrt(17))^n), with n >= 0. - Paolo P. Lava, Jul 31 2009

MATHEMATICA

LinearRecurrence[{5, -2}, {5, 21}, 50] (* G. C. Greubel, Jun 27 2018 *)

PROG

(PARI) x='x+O('x^30); Vec(-(-5+4*x)/(1-5*x+2*x^2)) \\ G. C. Greubel, Jun 27 2018

(MAGMA) I:=[5, 21]; [n le 2 select I[n] else 5*Self(n-1) - 2*Self(n-2): n in [1..30]]; // G. C. Greubel, Jun 27 2018

CROSSREFS

Cf. A107839.

Sequence in context: A103519 A178876 A202513 * A201869 A017968 A017969

Adjacent sequences:  A159286 A159287 A159288 * A159290 A159291 A159292

KEYWORD

nonn,easy

AUTHOR

Creighton Dement, Apr 08 2009

STATUS

approved

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Last modified November 15 04:00 EST 2018. Contains 317225 sequences. (Running on oeis4.)