A164611 Expansion of (1 + x + 2*x^2 - x^3)/(1 - 2*x + 3*x^2 - 2*x^3 + x^4).

1, 3, 5, 2, -6, -11, -5, 9, 17, 8, -12, -23, -11, 15, 29, 14, -18, -35, -17, 21, 41, 20, -24, -47, -23, 27, 53, 26, -30, -59, -29, 33, 65, 32, -36, -71, -35, 39, 77, 38, -42, -83, -41, 45, 89, 44, -48, -95, -47, 51, 101

Offset: 0

Author

Paul Barry, Aug 17 2009

Keywords

• easy
• sign

Comments

Hankel transform of A113682.

Links

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

Programs

Mathematica

CoefficientList[Series[(1+x+2x^2-x^3)/(1-2x+3x^2-2x^3+x^4),{x,0,80}],x] (* or *) LinearRecurrence[{2,-3,2,-1},{1,3,5,2},80] (* Harvey P. Dale, May 28 2013 *)

PARI

x='x+O('x^50); Vec((1 +x +2*x^2 -x^3)/(1 -2*x +3*x^2 -2*x^3 +x^4)) \\ G. C. Greubel, Aug 10 2017

Formula

G.f.: (1+x+2*x^2-x^3)/(1-x+x^2)^2.

a(n) = 2*a(n-1)-3*a(n-2)+2*a(n-3)-a(n-4), with a(0)=1, a(1)=3, a(2)=5, a(3)=2. - Harvey P. Dale, May 28 2013