A115054 G.f.: (x^3+6*x+2)^2/(x^2+x+1)^2.

4, 16, -8, -36, 72, -36, -63, 126, -63, -90, 180, -90, -117, 234, -117, -144, 288, -144, -171, 342, -171, -198, 396, -198, -225, 450, -225, -252, 504, -252, -279, 558, -279, -306, 612, -306, -333, 666, -333, -360, 720, -360, -387, 774, -387, -414, 828, -414, -441, 882, -441, -468, 936, -468, -495, 990, -495

Offset: 0

Author

Roger L. Bagula, Feb 28 2006

Keywords

• sign
• easy

Comments

q=3 coefficient expansion of hierarchical lattice renormalization polynomial.

Auto-convolution of the sequence 2,4,-6,3,3,-6,3,3,.. (period length 3). [From R. J. Mathar, Mar 09 2009]

References

• Peitgen and Richter, The Beauty of Fractals, Springer-Verlag, New York, 1986, page 146

Links

• Index entries for linear recurrences with constant coefficients, signature (-2,-3,-2,-1).

Programs

Maple

G:=(x^3+6*x+2)^2/(x^2+x+1)^2: Gser:=series(G,x=0,55): seq(coeff(Gser,x,n),n=0..50);

Mathematica

q=3 b = 9*Flatten[{{4/9}, Abs[Table[Coefficient[ Series[((x^3 + 3*(q - 1)*x + (q - 1)*(q - 2))/(3*x^2 + 3*( q - 2)*x + q^2 - 3*q + 3))^2, {x, 0, 30}], x^n], {n, 1, 30}]]}]

Formula

a(n) = 18*A131713(n)-27*(-1)^n*A099254(n), n>2. [From R. J. Mathar, Mar 09 2009]

Extensions

Edited by N. J. A. Sloane, Apr 16 2006