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A189732 a(1)=1,  a(2)=5, a(n) = a(n-1) + 5*a(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

Silvana Ramaj, New Results on Cyclic Compositions and Multicompositions, Master's Thesis, Georgia Southern Univ., 2021. See p. 33.

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..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: A214650 A032772 A326232 * A307607 A174933 A270219

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 September 26 00:53 EDT 2022. Contains 356986 sequences. (Running on oeis4.)