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A115054
G.f.: (x^3+6*x+2)^2/(x^2+x+1)^2.
0
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
0,1
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
FORMULA
a(n) = 18*A131713(n)-27*(-1)^n*A099254(n), n>2. [From R. J. Mathar, Mar 09 2009]
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}]]}]
CROSSREFS
Sequence in context: A335353 A110651 A253890 * A228561 A049208 A316274
KEYWORD
sign,easy
AUTHOR
Roger L. Bagula, Feb 28 2006
EXTENSIONS
Edited by N. J. A. Sloane, Apr 16 2006
STATUS
approved