A143769 Expansion of 3*x*(3*x+1)*(2*x-1) / ( (1+x)*(3*x^2+1) ).

-3, 0, 27, -18, -63, 36, 207, -126, -603, 360, 1827, -1098, -5463, 3276, 16407, -9846, -49203, 29520, 147627, -88578, -442863, 265716, 1328607, -797166, -3985803, 2391480, 11957427, -7174458, -35872263, 21523356, 107616807, -64570086, -322850403, 193710240

Offset: 1

Author

Paul Curtz, Aug 31 2008

Keywords

• sign
• easy

Comments

All entries are multiples of 3.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,-3,-3)

Programs

Magma

I:=[-3,0,27]; [n le 3 select I[n] else -Self(n-1)-3*Self(n-2) -3*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Aug 17 2013

Mathematica

CoefficientList[Series[3 (3 x + 1) (2 x - 1) / ((1 + x) (3 x^2 + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 17 2013 *)
LinearRecurrence[{-1,-3,-3},{-3,0,27},40] (* Harvey P. Dale, Dec 26 2014 *)

PARI

a(n)=3/2*((2*(-1)^n-3)*(-3)^floor(n/2)-3*(-1)^n); \\ Ralf Stephan, Aug 17 2013

Formula

a(n) = A141533(n+1)-2*A141533(n).

a(2n)+a(2n+1) = (-1)^n*A000244(n).

a(n) = (3/2) * ((2*(-1)^n - 3) * (-3)^floor(n/2) - 3*(-1)^n ). - Ralf Stephan, Aug 17 2013