A187062 Expansion of 2*x^2 *(4 +7*x +5*x^2 -x^3 -4*x^4 +6*x^6 +4*x^7 -x^8 -2*x^9) / ((1+x)^2 *(1+x+x^2)^2 *(1-x)^4) .

0, 0, 8, 14, 26, 42, 64, 90, 134, 172, 232, 300, 378, 464, 584, 690, 834, 990, 1160, 1342, 1574, 1784, 2048, 2328, 2626, 2940, 3320, 3670, 4090, 4530, 4992, 5474, 6038, 6564, 7176, 7812, 8474, 9160, 9944, 10682, 11522, 12390, 13288, 14214

Offset: 1

Author

Sean A. Irvine, Mar 21 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2,2,-1,-4,-1,2,2,0,-1).

Crossrefs

Cf. A000755, A178465, A187397, A225606.

Programs

Mathematica

CoefficientList[Series[ 2x^2 (4 + 7x + 5x^2 - x^3 - 4x^4 + 6x^6 + 4x^7 - x^8 - 2x^9)/((1 + x)^2 (1 + x + x^2)^2 (x - 1)^4), {x, 0, 43}], x]  (* or *) LinearRecurrence[ {0, 2, 2, -1, -4, -1, 2, 2, 0, -1}, {8, 14, 26, 42, 64, 90, 134, 172, 232, 300}, 42] (* Robert G. Wilson v, Feb 17 2014 *)

Formula

a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) - 4*a(n-5) - a(n-6) + 2*a(n-7) + 2*a(n-8) - a(n-10) .

Extensions

Name replaced by L. Edson Jeffery's definition. R. J. Mathar, Aug 06 2013