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A122047
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Degree of the polynomial P(n,x), defined by a Somos-6 type sequence: P(n,x)=(x^(n-1)*P(n-1,x)*P(n-5,x) + P(n-2,x)*P(n-4,x))/P(n-6,x), initialized with P(n,x)=1 at n<0.
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4
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0, 0, 1, 3, 6, 10, 15, 22, 31, 42, 55, 70, 88, 109, 133, 160, 190, 224, 262, 304, 350, 400, 455, 515, 580, 650, 725, 806, 893, 986, 1085, 1190, 1302, 1421, 1547, 1680, 1820, 1968, 2124, 2288, 2460, 2640, 2829, 3027
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| A. N. W. Hone, Algebraic curves, integer sequences and a discrete Painleve transcendent, Proceedings of SIDE 6, Helsinki, Finland, 2004. [Set a(n)=d(n+3) on p. 8]
Brian OSullivan and Thomas Busch, Spontaneous emission in ultra-cold spin-polarised anisotropic Fermi seas, arXiv 0810.0231v1 [quant-ph], 2008. [Eq 10a, lambda=5]
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FORMULA
| Conjecture: a(n)=3*a(n-1)-3*a(n-2)+a(n-3)+a(n-5)-3*a(n-6)+3*a(n-7)-a(n-8). O.g.f.: x^2/((x^4+x^3+x^2+x+1)(x-1)^4). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 15 2008
Conjecture: a(n)=(A000292(n+1)-n-2-(-1)^[(n-1)/5]*A099443(n+1))/5. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 15 2008
a(n+2) = A144679(n) + A144679(n-1) + A144679(n-2) + A144679(n-3) + A144679(n-4) [Johannes W. Meijer, May 20 2011]
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MATHEMATICA
| p[n_] := p[n] = Cancel[Simplify[(x^(n - 1)p[n - 1]p[n - 5] + p[n - 2]*p[n - 4])/p[n - 6]]]; 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, 20}]
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CROSSREFS
| Cf. A014125, A122046.
Sequence in context: A117245 A011914 A173645 * A177100 A137358 A143963
Adjacent sequences: A122044 A122045 A122046 * A122048 A122049 A122050
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KEYWORD
| nonn
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 13 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 15 2008
a(22)-a(43) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 15 2008
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