A077849 Expansion of (1-x)^(-1)/(1 - 2*x - x^2 - x^3).

1, 3, 8, 21, 54, 138, 352, 897, 2285, 5820, 14823, 37752, 96148, 244872, 623645, 1588311, 4045140, 10302237, 26237926, 66823230, 170186624, 433434405, 1103878665, 2811378360, 7160069791, 18235396608, 46442241368, 118279949136, 301237536249, 767197263003

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

Links

• I. M. Gessel, Ji Li, Compositions and Fibonacci identities, J. Int. Seq. 16 (2013) 13.4.5
• Index entries for linear recurrences with constant coefficients, signature (3,-1,0,-1)

Crossrefs

Partial sums of A077939.

Programs

Maple

A077939 := proc(n) if n< 0 then 0; else coeftayl( 1/(1-2*x-x^2-x^3) ,x=0,n) ; end if; end proc:
A077849 := proc(n) (-1+4*A077939(n)+2*A077939(n-1)+A077939(n-2))/3 ; end proc:
seq(A077849(n),n=0..20) ; # R. J. Mathar, Mar 22 2011

Mathematica

CoefficientList[Series[(1-x)^(-1)/(1-2x-x^2-x^3),{x,0,40}],x] (* or *) LinearRecurrence[{3,-1,0,-1},{1,3,8,21},40] (* Harvey P. Dale, Nov 01 2016 *)

PARI

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