A077864 Expansion of (1-x)^(-1)/(1-x-2*x^2-x^3).

1, 2, 5, 11, 24, 52, 112, 241, 518, 1113, 2391, 5136, 11032, 23696, 50897, 109322, 234813, 504355, 1083304, 2326828, 4997792, 10734753, 23057166, 49524465, 106373551, 228479648, 490751216, 1054084064, 2264066145, 4862985490, 10445201845, 22435238971, 48188628152

Offset

0,2

Comments

Diagonal sums of triangle using cumulative sums of odd-indexed rows of Pascal's triangle (cf. A020988). - Paul Barry, May 18 2003

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2, 1, -1, -1).

Formula

a(0)=1, a(1)=2, a(2)=5, a(3)=11, a(n)=2*a(n-1)+a(n-2)-a(n-3)-a(n-4) for n>3. - Philippe Deléham, Oct 25 2006

a(n) = term (4,1) in the 4x4 matrix [1,1,0,0; 2,0,1,0; 1,0,0,0; 1,0,0,1]^(n+1). - Alois P. Heinz, Jul 24 2008

Conjecture: a(n) = Sum_{j=0..n/2} A027907(n+1-j,2*j+1), n >= 0. - Werner Schulte, Sep 29 2015

Maple

a := n -> (Matrix([[1, 1, 0, 0], [2, 0, 1, 0], [1, 0, 0, 0], [1, 0, 0, 1]])^(n+1))[4, 1]; seq(a(n), n=0..50);  # Alois P. Heinz, Jul 24 2008

Mathematica

CoefficientList[Series[(1-x)^(-1)/(1-x-2x^2-x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{2, 1, -1, -1}, {1, 2, 5, 11}, 40] (* Harvey P. Dale, Oct 08 2014 *)

Prog

(PARI) Vec((1-x)^(-1)/(1-x-2*x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Sequence in context: A286945 A350326 A111297 * A052980 A190512 A110513

Adjacent sequences: A077861 A077862 A077863 * A077865 A077866 A077867

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved