A200563 Expansion of -2*x*(1+4*x) / ((2*x-1)*(4*x^2+3*x+1)).

2, 6, -2, 30, 14, 30, 238, -66, 782, 990, 46, 8190, -178, 16926, 48238, -15810, 247694, 106590, 262318, 1932414, -555058, 6518430, 7830766, 765630, 67043342, -2865954, 143077678, 387537150, -124309426, 2044005150, 807673198, 2285861694, 15681525902, -4648416930

Offset: 1

Author

Krishnamurthy Balasubraniam, Nov 19 2011

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,2,8).

Programs

Magma

I:=[2, 6, -2]; [n le 3 select I[n] else -Self(n-1)+2*Self(n-2)+8*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 12 2012

Mathematica

LinearRecurrence[{-1,2,8}, {2,6,-2},34] (* Bruno Berselli, Dec 12 2011 *)

Maxima

makelist(expand((6*4^n+(-3-sqrt(-7))^(n+1)+(-3+sqrt(-7))^(n+1))/(7*2^n)),n,1,34); /* Bruno Berselli, Dec 12 2011 */

Formula

a(n) = -a(n-1) +2*a(n-2) +8*a(n-3).

a(n) = (6*4^n+r^(n+1)+(16/r)^(n+1))/(7*2^n), where r=-3-sqrt(-7). - Bruno Berselli, Dec 12 2011

Extensions

Definition from R. J. Mathar, Nov 19 2011