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

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

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

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 */
(PARI) a(n)=([0, 1; 5, 1]^(n-1)*[1; 5])[1, 1] \\ Charles R Greathouse IV, Oct 21 2022

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,easy

Author

Harvey P. Dale, Apr 26 2011

Status

approved