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

Author

Harvey P. Dale, Apr 26 2011

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Mathematica

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

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

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