A138341 Expansion of (1-4x-x^3)/(1-x+x^2)^2.

1, -2, -7, -7, 2, 13, 13, -2, -19, -19, 2, 25, 25, -2, -31, -31, 2, 37, 37, -2, -43, -43, 2, 49, 49, -2, -55, -55, 2, 61, 61, -2, -67, -67, 2, 73, 73, -2, -79, -79, 2, 85, 85, -2, -91, -91, 2, 97, 97, -2, -103, -103, 2, 109, 109, -2, -115, -115, 2, 121, 121, -2

Offset: 0

Author

Paul Barry, Mar 15 2008

Keywords

• sign
• easy

Comments

Hankel transform of A079309.

Links

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

Crossrefs

Cf. A079309, A138342.

Programs

Mathematica

CoefficientList[Series[(1-4x-x^3)/(1-x+x^2)^2,{x,0,100}],x] (* or *) LinearRecurrence[{2,-3,2,-1},{1,-2,-7,-7},100] (* Harvey P. Dale, Sep 23 2021 *)

PARI

Vec((1-4*x-x^3)/(1-x+x^2)^2 + O(x^62)) \\ Jinyuan Wang, Apr 09 2020

Formula

a(n) = (2n+1)*cos(Pi*n/3) - (2n+5)*sin(Pi*n/3)/sqrt(3).

a(n) = 2*a(n-1) - 3*a(n-2) + 2*a(n-3) - a(n-4) for n > 3. - Jinyuan Wang, Apr 09 2020

Extensions

More terms from Jinyuan Wang, Apr 09 2020