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A122056 A Somos 9-Hone exponent type recursion: a(n) = (x^(n-1)*a(n - 1)a(n - 8) - a(n - 4)*a(n - 5))/a(n - 9). 0
0, 0, 1, 3, 6, 10, 15, 21, 28, 36, 46, 58, 72, 88, 106, 126, 148, 172, 199, 229, 262, 298, 337, 379, 424, 472, 524, 580, 640, 704, 772 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..31.

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]

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).

Conjectures from Colin Barker, Oct 08 2019: (Start)

G.f.: x^3 / ((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)

MATHEMATICA

p[n_] := p[n] = Cancel[Simplify[(x^(n - 1)p[n - 1]p[n - 8] + p[n - 4]*p[n - 5])/p[n - 9]]]; p[ -9] = 1; p[ -8] = 1; p[ -7] = 1; p[ -6] = 1; p[ -5] = 1; p[ -4] = 1; p[ -3] = 1; p[ -2] = 1; p[ -1] = 1; Table[Exponent[p[n], x], {n, 0, 30}]

CROSSREFS

Cf. A006731, A014125.

Sequence in context: A194153 A025737 A120721 * A025706 A025730 A066353

Adjacent sequences:  A122053 A122054 A122055 * A122057 A122058 A122059

KEYWORD

nonn,uned,more

AUTHOR

Roger L. Bagula, Sep 13 2006

STATUS

approved

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Last modified October 21 05:21 EDT 2021. Contains 348141 sequences. (Running on oeis4.)