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A189732 a(1)=1,  a(2)=5, a(n)=a(n-1) + 5a(n-2). 14
1, 5, 10, 35, 85, 260, 685, 1985, 5410, 15335, 42385, 119060, 330985, 926285, 2581210, 7212635, 20118685, 56181860, 156775285, 437684585, 1221561010, 3409983935, 9517788985, 26567708660, 74156653585, 206995196885, 577778464810, 1612754449235, 4501646773285 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

Index entries for linear recurrences with constant coefficients, signature (1, 5).

FORMULA

a(n) = 1/2*((1/2+1/2*sqrt(21))^(n-1)+(1/2-1/2*sqrt(21))^(n-1)+3/14*sqrt(21)*((1/2+1/2 *sqrt(21))^(n-1)-(1/2-1/2*sqrt(21))^(n-1)). - Paolo P. Lava, May 24 2011

G.f.: x*(1+4*x)/(1-x-5*x^2). - Bruno Berselli, May 24 2011

a(n+1) = Sum_{k, 0<=k<=n} A119473(n,k)*4^k. - Philippe Deléham, Oct 05 2012

MATHEMATICA

LinearRecurrence[{1, 5}, {1, 5}, 40]

PROG

(Maxima) a[1]:1$ a[2]:5$ a[n]:=a[n-1]+5*a[n-2]$ makelist(a[n], n, 1, 29);  [Bruno Berselli, May 24 2011]

CROSSREFS

Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189734, A189735, A189736, A189737, A189738, A189739, A189741, A189742,A189743, A189744, A189745, A189746, A189747, A189748, A189749.

Sequence in context: A121158 A214650 A032772 * A174933 A270219 A270276

Adjacent sequences:  A189729 A189730 A189731 * A189733 A189734 A189735

KEYWORD

nonn

AUTHOR

Harvey P. Dale, Apr 26 2011

STATUS

approved

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Last modified November 20 08:12 EST 2017. Contains 294962 sequences.