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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

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

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.

Adjacent sequences: A006720 A006721 A006722 this_sequence A006724 A006725 A006726

Sequence in context: A099170 A018095 A003217 this_sequence A096390 A092264 A135729

KEYWORD

nonn,easy,nice

AUTHOR

njas

EXTENSIONS

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

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Last modified October 12 15:26 EDT 2008. Contains 144830 sequences.


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