A167617 G.f.: x^2*(3+3*x+x^2) / ( (2*x+1) * (1+x) * (1+x+x^2) * (x^2-x+1) ) .

0, 0, 3, -6, 10, -21, 42, -84, 171, -342, 682, -1365, 2730, -5460, 10923, -21846, 43690, -87381, 174762, -349524, 699051, -1398102, 2796202, -5592405, 11184810, -22369620, 44739243, -89478486, 178956970, -357913941, 715827882, -1431655764, 2863311531

Offset: 0

Author

Paul Curtz, Nov 07 2009

Keywords

• sign
• easy

Comments

The derived sequence a(n+1) + 2*a(n) reads 0,3,0,-2,-1,0 (and repeat with period 6).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-3, -3, -3, -3, -3, -2).

Crossrefs

Cf. A167613.

Programs

Mathematica

CoefficientList[Series[x^2(3+3x+x^2)/((2x+1)(1+x)(1+x+x^2)(x^2-x+1)), {x,0,40}],x] (* or *) LinearRecurrence[{-3,-3,-3,-3,-3,-2},{0,0,3,-6,10,-21},40] (* Harvey P. Dale, Sep 08 2011 *)

Formula

a(3*k+2) + a(3*k+3) + a(3*k+4) = (-1)^(k+1)*A024088(k+1).

a(n) = (-1)^n*A024495(n+1) + A131531(n+1).

a(n) = -3*a(n-1) -3*a(n-2) -3*a(n-3) -3*a(n-4) -3*a(n-5) -2*a(n-6).

Extensions

Edited and extended by R. J. Mathar, Nov 12 2009