A199853 Expansion of (1-3*x+x^3)/(1-2*x-x^2+x^3).

1, -1, -1, -3, -6, -14, -31, -70, -157, -353, -793, -1782, -4004, -8997, -20216, -45425, -102069, -229347, -515338, -1157954, -2601899, -5846414, -13136773, -29518061, -66326481, -149034250, -334876920, -752461609, -1690765888, -3799116465, -8536537209

Offset: 0

Author

Philippe Deléham, Nov 11 2011

Keywords

• sign
• easy

Links

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

Crossrefs

Cf. A006356, A077998, A180262.

Programs

Mathematica

RecurrenceTable[{a[1]==-1, a[2]== -1, a[3]== -3, a[n]== 2*a[n-1]  + a[n-2] - a[n-3]}, a, {n,30}] (* G. C. Greubel, Aug 13 2015 *)
CoefficientList[Series[(1-3x+x^3)/(1-2x-x^2+x^3),{x,0,30}],x] (* or *) LinearRecurrence[{2,1,-1},{1,-1,-1,-3},40] (* Harvey P. Dale, May 31 2021 *)

PARI

Vec((1-3*x+x^3)/(1-2*x-x^2+x^3) + O(x^40)) \\ Michel Marcus, Aug 13 2015

Formula

a(n) = 2*a(n-1) + a(n-2) - a(n-3) with a(0)=1, a(1)=-1, a(2)=-1, a(3)=-3.

a(n+1) = - A077998(n). - G. C. Greubel, Aug 14 2015