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Search: id:A006723
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| A006723 |
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Somos-7 sequence: a(n) = (a(n-1)a(n-6) + a(n-2)a(n-5) + a(n-3)a(n-4)) / a(n-7).
(Formerly M2456)
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+0
9
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| 1, 1, 1, 1, 1, 1, 1, 3, 5, 9, 17, 41, 137, 769, 1925, 7203, 34081, 227321, 1737001, 14736001, 63232441, 702617001, 8873580481, 122337693603, 1705473647525, 22511386506929, 251582370867257, 9254211194697641, 215321535159114017
(list; graph; listen)
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OFFSET
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0,8
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. H. Buchholz and R. L. Rathbun, "An infinite set of Heron triangles with two rational medians", Amer. Math. Monthly, 104 (1997), 107-115.
David Gale, "The strange and surprising saga of the Somos sequence", Math. Intelligencer 13(1) (1991), pp. 40-42.
J. L. Malouf, "An integer sequence from a rational recursion", Discr. Math. 110 (1992), 257-261.
R. M. Robinson, "Periodicity of Somos sequences", Proc. Amer. Math. Soc., 116 (1992), 613-619.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
Index entries for two-way infinite sequences
S. Fomin and A. Zelevinsky, The Laurent phenomemon
J. Propp, The Somos Sequence Site
M. Somos, Somos 6 Sequence
M. Somos, Brief history of the Somos sequence problem
A. van der Poorten, Hyperelliptic curves, continued fractions and Somos sequences
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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PROGRAM
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(PARI) a(n)=if(n<0, a(6-n), if(n<7, 1, (a(n-1)*a(n-6)+a(n-2)*a(n-5)+a(n-3)*a(n-4))/a(n-7)))
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CROSSREFS
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Cf. A006720, A006721, A006722, A048736.
Sequence in context: A099170 A018095 A003217 this_sequence A096390 A092264 A135729
Adjacent sequences: A006720 A006721 A006722 this_sequence A006724 A006725 A006726
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 22 2000
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