|
Search: id:A122047
|
|
|
| A122047 |
|
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. |
|
+0
2
|
|
| 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; listen)
|
|
|
OFFSET
|
0,4
|
|
|
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]
|
|
FORMULA
|
Conjecture: a(n)=3a(n-1)-3a(n-2)+a(n-3)+a(n-5)-3a(n-6)+3a(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
|
|
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}]
|
|
CROSSREFS
|
Cf. A014125, A122046.
Adjacent sequences: A122044 A122045 A122046 this_sequence A122048 A122049 A122050
Sequence in context: A024918 A117245 A011914 this_sequence A137358 A143963 A139714
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 13 2006
|
|
EXTENSIONS
|
Edited by njas, Jul 15 2008
a(22)-a(43) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 15 2008
|
|
|
Search completed in 0.002 seconds
|
