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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved