A115053 - OEIS

A115053

Series expansion of x*(x+3)^2/(3*x+1)^2.

0, 9, -48, 208, -816, 3024, -10800, 37584, -128304, 431568, -1434672, 4723920, -15431472, 50073552, -161558064, 518686416, -1658095920, 5280397776, -16759523376, 53033560272, -167365651248, 526891865040, -1655060329008, 5188335188688, -16234468171056, 50711792328144

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OFFSET

0,2

COMMENTS

Expansion of q=2 hierarchical lattice renormalization polynomial.

REFERENCES

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

LINKS

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (-6,-9).

FORMULA

For n>1, a(n) = 16 * (4n+1) * (-3)^(n-3). - Ralf Stephan, Jul 19 2013

MATHEMATICA

q=2 b = Delete[Union[Flatten[{{0}, 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}]]}]], 1]

CROSSREFS

Sequence in context: A055582 A359175 A054460 * A181959 A171011 A264273

Adjacent sequences: A115050 A115051 A115052 * A115054 A115055 A115056

KEYWORD

sign

AUTHOR

Roger L. Bagula, Feb 28 2006

EXTENSIONS

Edited by N. J. A. Sloane, Dec 31 2006

STATUS

approved