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A006722
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Somos-6 sequence: a(n) = (a(n-1) * a(n-5) + a(n-2) * a(n-4) + a(n-3)^2) / a(n-6), a(0) = ... = a(5) = 1.
(Formerly M2457)
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13
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1, 1, 1, 1, 1, 1, 3, 5, 9, 23, 75, 421, 1103, 5047, 41783, 281527, 2534423, 14161887, 232663909, 3988834875, 45788778247, 805144998681, 14980361322965, 620933643034787, 16379818848380849, 369622905371172929
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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REFERENCES
| 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 sequences", Math. Intelligencer 13(1) (1991), pp. 40-42.
J. L. Malouf, "An integer sequence from a rational recursion", Discr. Math. 110 (1992), 257-261.
C. Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 350.
R. M. Robinson, "Periodicity of Somos sequences", Proc. Amer. Math. Soc., 116 (1992), 613-619.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
S. Fomin and A. Zelevinsky, The Laurent phenomemon
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.
Index entries for two-way infinite sequences
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FORMULA
| a(5-n) = a(n).
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PROG
| (PARI) {a(n) = if( n>-1 && n<6, 1, if( n<0, a(5 - n), (a(n - 1) * a(n - 5) + a(n - 2) * a(n - 4) + a(n-3) * a(n-3)) / a(n - 6)))} /* Michael Somos, Jan 30 2012 */
(Haskell)
a006722 n = a006722_list !! n
a006722_list = [1, 1, 1, 1, 1, 1] ++
zipWith div (foldr1 (zipWith (+)) (map b [1..3])) a006722_list
where b i = zipWith (*) (drop i a006722_list) (drop (6-i) a006722_list)
-- Reinhard Zumkeller, Jan 22 2012
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CROSSREFS
| Cf. A006720, A006721, A006723, A048736.
Sequence in context: A146275 A089636 A083366 * A039774 A114001 A171879
Adjacent sequences: A006719 A006720 A006721 * A006723 A006724 A006725
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 22 2000
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