A077922 Expansion of (1-x)^(-1)/(1+2*x-x^2+x^3).

1, -1, 4, -9, 24, -60, 154, -391, 997, -2538, 6465, -16464, 41932, -106792, 271981, -692685, 1764144, -4492953, 11442736, -29142568, 74220826, -189026955, 481417305, -1226082390, 3122609041, -7952717776, 20254126984, -51583580784, 131374006329, -334585720425, 852129027964

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (-1,3,-2,1)

Crossrefs

Cf. A010907.

Programs

Maple

A077986 := proc(n) if n < 0 then 0; else coeftayl( 1/(1+2*x-x^2+x^3),x=0,n) ; end if; end proc:
A077922 := proc(n) (1+2*A077986(n)+A077986(n-2))/3 ; end proc:
seq(A077922(n),n=0..20) ; # R. J. Mathar, Mar 24 2011

Mathematica

CoefficientList[Series[1/((1 + 2*x - x^2 + x^3)(1 - x)), {x, 0, 30}], x]
LinearRecurrence[{-1,3,-2,1},{1,-1,4,-9},40] (* Harvey P. Dale, Feb 10 2024 *)

PARI

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

Formula

a(n) = (1 + 2*A077986(n) + A077986(n-2))/3. - R. J. Mathar