A077850 Expansion of (1-x)^(-1)/(1 - 2*x - x^2 + x^3).

1, 3, 8, 19, 44, 100, 226, 509, 1145, 2574, 5785, 13000, 29212, 65640, 147493, 331415, 744684, 1673291, 3759852, 8448312, 18983186, 42654833, 95844541, 215360730, 483911169, 1087338528, 2443227496, 5489882352, 12335653673, 27717962203, 62281695728, 139945699987

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

Comments

a(n) = A052534(n+1) - 1.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3, -1, -2, 1).

Crossrefs

Cf. A188106. See also A189247. - L. Edson Jeffery, Apr 22 2011

Programs

Mathematica

CoefficientList[Series[(1-x)^(-1)/(1-2x-x^2+x^3),{x,0,40}],x] (* or *) LinearRecurrence[{3,-1,-2,1},{1,3,8,19},40] (* Harvey P. Dale, Jan 22 2013 *)

PARI

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

Formula

a(n) = sum(k=0..n+2, A006054(k)). - Philippe Deléham, Sep 07 2006

a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) + a(n-4), n>3. Also a(n)=Sum_{k=0..n} A188106(n,k), n=0,1,2,..., giving partial sums of first convolution of A006054 with itself. - L. Edson Jeffery, Apr 22 2011