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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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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
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.
Adjacent sequences: A006720 A006721 A006722 this_sequence A006724 A006725 A006726
Sequence in context: A099170 A018095 A003217 this_sequence A096390 A092264 A135729
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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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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