OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
A. N. W. Hone, Algebraic curves, integer sequences and a discrete Painlevé transcendent, arXiv:0807.2538 [nlin.SI], 2008; Proceedings of SIDE 6, Helsinki, Finland, 2004. [Set a(n)=d(n+3) on p. 8]
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,1,-3,3,-1).
FORMULA
a(n) = degree(p(n)) with p(n) = (x^(n-1)*p(n-1)*p(n-8) + p(n-4)*p(n-5))/p(n-9).
From Colin Barker, Oct 08 2019: (Start)
G.f.: x^2 / ((1-x)^4*(1+x)*(1+x^2)*(1+x^4)).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-8) - 3*a(n-9) + 3*a(n-10) - a(n-11) for n > 10. (End)
a(n) = (1/192)*(4*n^3 +42*n^2 +80*n -63 +3*(-1)^n) + (1/32)*(i^n*(1 + (-1)^n) + i^(n+1)*(1-(-1)^n)) + (1/4)*(b(n) -b(n-1) -2*b(n-2) -2*b(n -3)), where b(n) = A014017(n). - G. C. Greubel, Dec 29 2022
MATHEMATICA
p[n_]:= p[n] = If[n<0, 1, Cancel[Simplify[(x^(n-1)*p[n-1]*p[n-8] + p[n-4]*p[n-5])/p[n-9]]]]; Table[Exponent[p[n], x], {n, 0, 30}]
LinearRecurrence[{3, -3, 1, 0, 0, 0, 0, 1, -3, 3, -1}, {0, 0, 1, 3, 6, 10, 15, 21, 28, 36, 46, 58, 72}, 61] (* G. C. Greubel, Dec 29 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 72); [0, 0] cat Coefficients(R!( x^2/((1-x)^4*(1+x)*(1+x^2)*(1+x^4)) )); // G. C. Greubel, Dec 29 2022
(SageMath)
def A122056_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x^2/((1-x)^4*(1+x)*(1+x^2)*(1+x^4)) ).list()
A122056_list(70) # G. C. Greubel, Dec 29 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Sep 13 2006
EXTENSIONS
Edited by G. C. Greubel, Dec 29 2022
STATUS
approved