A120775 a(n) = 3*a(n-1) + 5*a(n-2) + a(n-3).

1, 6, 23, 100, 421, 1786, 7563, 32040, 135721, 574926, 2435423, 10316620, 43701901, 185124226, 784198803, 3321919440, 14071876561, 59609425686, 252509579303, 1069647742900, 4531100550901, 19194049946506, 81307300336923

Offset

1,2

Links

Table of n, a(n) for n=1..23.

Index entries for linear recurrences with constant coefficients, signature (3,5,1).

Formula

a(n) = 3*a(n-1) + 5*a(n-2) + a(n-3).

G.f. -x*(1+3*x) / ( (1+x)*(x^2+4*x-1) ). a(n) + a(n+1) = A048876(n). - R. J. Mathar, Oct 22 2013

a(n) = (Lucas(3n-1) + (-1)^n)/2. - Greg Dresden, Oct 09 2020

Crossrefs

Cf. A120758, A120757.

Sequence in context: A220372 A321715 A038383 * A013258 A013264 A369835

Adjacent sequences: A120772 A120773 A120774 * A120776 A120777 A120778

Keyword

nonn,easy

Author

Gary W. Adamson and Roger L. Bagula, Jul 04 2006

Extensions

Edited by N. J. A. Sloane, Dec 03 2006

Status

approved