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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), a(0) = ... = a(6) = 1.
(Formerly M2456)
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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; refs; listen; history; internal format)
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OFFSET
| 0,8
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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.
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
J. Propp, The Somos Sequence Site
M. Somos, Somos 7 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(6 - n) = a(n).
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MATHEMATICA
| RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==a[4]==a[5]==a[6]==1, a[n] == (a[n-1]a[n-6]+a[n-2]a[n-5]+a[n-3]a[n-4])/a[n-7]}, a, {n, 30}] (* From Harvey P. Dale, Jan 19 2012 *)
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PROG
| (PARI) {a(n) = local(v); if( n<0, n = 6-n); if( n<7, 1, n++; v = vector(n, k, 1); for( k=8, n, v[k] = (v[k-1] * v[k-6] + v[k-2] * v[k-5] + v[k-3] * v[k-4]) / v[k-7]); v[n])}
(Haskell)
a006723 n = a006723_list !! n
a006723_list = [1, 1, 1, 1, 1, 1, 1] ++
zipWith div (foldr1 (zipWith (+)) (map b [1..3])) a006723_list
where b i = zipWith (*) (drop i a006723_list) (drop (7-i) a006723_list)
-- Reinhard Zumkeller, Jan 22 2012
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CROSSREFS
| Cf. A006720, A006721, A006722, A048736.
Sequence in context: A018095 A003217 A178717 * A096390 A092264 A135729
Adjacent sequences: A006720 A006721 A006722 * A006724 A006725 A006726
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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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