A123102 a(0)=1, a(1)=0, a(2)=1, a(n) = a(n-1) + a(n-2) + 3*a(n-3).

1, 0, 1, 4, 5, 12, 29, 56, 121, 264, 553, 1180, 2525, 5364, 11429, 24368, 51889, 110544, 235537, 501748, 1068917, 2277276, 4851437, 10335464, 22018729, 46908504, 99933625, 212898316, 453557453, 966256644, 2058509045, 4385438048

Offset

0,4

Links

Table of n, a(n) for n=0..31.

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

Formula

a(n) + a(n+1) = A099213(n+1).

G.f.: (1-x)/(1-x-x^2-3*x^3).

If p[1]=0, p[2]=1, p[i]=4, (i>2), and if A is Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise, then, for n>=1, a(n)=det A. - Milan Janjic, May 02 2010

Mathematica

LinearRecurrence[{1, 1, 3}, {1, 0, 1}, 40] (* Harvey P. Dale, May 04 2018 *)

Prog

(PARI) Vec((1-x)/(1-x-x^2-3*x^3) + O(x^40)) \\ Michel Marcus, Aug 07 2022

Crossrefs

Cf. A099213.

Sequence in context: A369697 A308775 A305335 * A274077 A028272 A003969

Adjacent sequences: A123099 A123100 A123101 * A123103 A123104 A123105

Keyword

nonn,easy

Author

Philippe Deléham, Sep 27 2006

Extensions

Corrected by T. D. Noe, Nov 07 2006

Status

approved