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A006723 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)
+0
9
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)
OFFSET

0,8

REFERENCES

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.

LINKS

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.

PROGRAM

(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)))

CROSSREFS

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

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 22 2000

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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