A108981 a(n) = 3a(n-1) + 4a(n-2), a(0) = 1, a(1) = 5.

1, 5, 19, 77, 307, 1229, 4915, 19661, 78643, 314573, 1258291, 5033165, 20132659, 80530637, 322122547, 1288490189, 5153960755, 20615843021, 82463372083, 329853488333, 1319413953331, 5277655813325, 21110623253299

Offset

0,2

Comments

The Hankel transform of this sequence is [1,-6,0,0,0,0,0,0,0,0,...]. - Philippe Deléham, Apr 15 2008

Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=-2, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n >= 1, a(n-1) = charpoly(A,2). - Milan Janjic, Jan 26 2010

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (3,4).

Formula

Inverse binomial transform of A003948.

a(2n) = 4a(2n-1) - 1; a(2n+1) = 4a(2n) + 1.

O.g.f.: (1+2*x)/((1+x)(1-4*x)). - R. J. Mathar, Apr 02 2008

Sum_{k=0..n} a(k) = A037481(n+1). - Philippe Deléham, Apr 15 2008

Mathematica

LinearRecurrence[{3, 4}, {1, 5}, 30] (* Harvey P. Dale, Feb 16 2014 *)

Prog

(PARI) Vec((1+2*x)/(1+x)/(1-4*x)+O(x^99)) \\ Charles R Greathouse IV, Jan 11 2012
(Magma) I:=[1, 5]; [n le 2 select I[n] else 3*Self(n-1)+4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Feb 17 2014

Crossrefs

Cf. A003948, A037481.

Sequence in context: A275859 A323269 A268815 * A228678 A149771 A149772

Adjacent sequences: A108978 A108979 A108980 * A108982 A108983 A108984

Keyword

nonn,easy

Author

Philippe Deléham, Jul 23 2005

Extensions

Corrected by T. D. Noe, Nov 07 2006

Edited by N. J. A. Sloane at the suggestion of R. J. Mathar, Apr 14 2008

Status

approved