A077882 Expansion of x/((1-x)*(1-x^2-2*x^3)).

0, 1, 1, 2, 4, 5, 9, 14, 20, 33, 49, 74, 116, 173, 265, 406, 612, 937, 1425, 2162, 3300, 5013, 7625, 11614, 17652, 26865, 40881, 62170, 94612, 143933, 218953, 333158, 506820, 771065, 1173137, 1784706, 2715268, 4130981, 6284681, 9561518, 14546644, 22130881, 33669681

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

Comments

a(n+1) gives diagonal sums of Riordan array (1/(1-x),x*(1+2*x)) and partial sums of A052947. - Paul Barry, Jul 18 2005

Links

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

Programs

Mathematica

a[0] = 0; a[1] = 1; a[2] = 1; a[3] = 2; a[n_Integer?Positive] := a[n] = a[n - 1] + a[n - 2] + a[n - 3] - 2a[n - 4]; aa = Table[a[n], {n, 0, 42}] (* Roger L. Bagula, Mar 25 2005 *)
CoefficientList[Series[x/((1-x)(1-x^2-2x^3)),{x,0,50}],x] (* or *) LinearRecurrence[{1,1,1,-2},{0,1,1,2},50] (* Harvey P. Dale, Aug 17 2017 *)

Formula

a(n) = a(n-1)+a(n-2)+a(n-3)-2*a(n-4). - Roger L. Bagula, Mar 25 2005

a(n+1) = Sum_{k=0..n} Sum_{j=0..floor(k/2)} C(j, k-2*j)*2^(k-2*j). - Paul Barry, Jul 18 2005

Extensions

Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar