A107388 Expansion of x*(3*x-1)*(2*x-1) / ( (1-x)*(1+x)*(x^2-4*x+1) ).

0, 1, -1, 2, 4, 21, 75, 286, 1064, 3977, 14839, 55386, 206700, 771421, 2878979, 10744502, 40099024, 149651601, 558507375, 2084377906, 7779004244, 29031639077, 108347552059, 404358569166, 1509086724600, 5631988329241, 21018866592359, 78443478040202

Offset: 0

Author

Roger L. Bagula, May 24 2005, corrected Sep 04 2008

Keywords

• sign
• easy

Comments

One of the components of the n-th power of the 4X4 matrix with rows (0,1,0,0), (0,0,1,0), (0,0,0,1), (1,4,0,-4) multiplied by the vector (0,1,1,2).

Links

• Index entries for linear recurrences with constant coefficients, signature (4,0,-4,1).

Programs

Mathematica

CoefficientList[Series[x(3x-1)(2x-1)/((1-x)(1+x)(x^2-4x+1)),{x,0,40}],x] (* or *) LinearRecurrence[ {4,0,-4,1},{0,1,-1,2},40] (* Harvey P. Dale, Jun 17 2023 *)

Formula

a(n) = (-1)^(n+1)+(3*A001353(n+1)-11*A001353(n)-1)/2. - R. J. Mathar, Jul 10 2012

a(n) -a(n-2) = A001834(n-3). - R. J. Mathar, Dec 17 2017

Extensions

Sign of a(2) flipped. - R. J. Mathar, Jul 10 2012