OFFSET
0,2
COMMENTS
q=1 coefficient expansion of hierarchical lattice renormalization polynomial.
REFERENCES
Heinz-Otto Peitgen and Peter Richter (editors), The Beauty of Fractals, Springer-Verlag, New York, 1986, p. 146.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (6,-15,18,-9).
FORMULA
From Stefano Spezia, Sep 01 2025: (Start)
a(n) = 3^(n/2)*((1 - n)*cos(n*Pi/6) + sqrt(3)*(3 + n)*sin(n*Pi/6)).
E.g.f.: exp(3*x/2)*(cos(sqrt(3)*x/2) + sqrt(3)*(3 + 2*x)*sin(sqrt(3)*x/2)). (End)
MAPLE
A115052 := proc(n) 1/(3*x^2-3*x+1)^2 ; coeftayl(%, x=0, n) ; end proc: # R. J. Mathar, Sep 17 2011
PROG
(Magma) I:=[1, 6, 21, 54]; [n le 4 select I[n] else 6*Self(n-1)-15*Self(n-2)+18*Self(n-3)-9*Self(n-4): n in [1..40]]; // Vincenzo Librandi, Sep 20 2011
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Roger L. Bagula, Feb 28 2006
STATUS
approved