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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), a(0) = ... = a(6) = 1. (Formerly M2456) 11
 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; text; internal format)
 OFFSET 0,8 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n=0..100 R. H. Buchholz and R. L. Rathbun, An infinite set of Heron triangles with two rational medians, Amer. Math. Monthly, 104 (1997), 107-115. Chang, Xiangke; Hu, Xingbiao, A conjecture based on Somos-4 sequence and its extension, Linear Algebra Appl. 436, No. 11, 4285-4295 (2012). S. Fomin and A. Zelevinsky, The Laurent phenomemon, arXiv:math/0104241 [math.CO], 2001. David Gale, The strange and surprising saga of the Somos sequences, Math. Intelligencer 13(1) (1991), pp. 40-42. R. W. Gosper and Richard C. Schroeppel, Somos Sequence Near-Addition Formulas and Modular Theta Functions, arXiv:math/0703470 [math.NT], 2007. J. L. Malouf, An integer sequence from a rational recursion, Discr. Math. 110 (1992), 257-261. J. Propp, The Somos Sequence Site R. M. Robinson, Periodicity of Somos sequences, Proc. Amer. Math. Soc., 116 (1992), 613-619. Vladimir Shevelev and Peter J. C. Moses, On a sequence of polynomials with hypothetically integer coefficients, arXiv preprint arXiv:1112.5715 [math.NT], 2011. M. Somos, Somos 7 Sequence A. van der Poorten, Hyperelliptic curves, continued fractions and Somos sequences, arXiv:math/0608247 [math.NT], 2006. Eric Weisstein's World of Mathematics, Somos Sequence. FORMULA a(6 - n) = a(n) for all n in Z. a(n) = ((8-2*(-1)^n)*a(n-5)*a(n-3)-a(n-4)^2)/a(n-8). - Bruno Langlois, Aug 09 2016 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}] (* Harvey P. Dale, Jan 19 2012 *) PROG (PARI)  {a(n) = my(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 (Python) from gmpy2 import divexact A006723 = [1, 1, 1, 1, 1, 1, 1] for n in range(7, 101): ....A006723.append(divexact(A006723[n-1]*A006723[n-6]+A006723[n-2]*A006723[n-5]+A006723[n-3]*A006723[n-4], A006723[n-7])) # Chai Wah Wu, Sep 01 2014 (MAGMA) I:=[1, 1, 1, 1, 1, 1, 1]; [n le 7 select I[n] else (Self(n-1)*Self(n-6) + Self(n-2)*Self(n-5) + Self(n-3)*Self(n-4))/Self(n-7): n in [1..30]]; // G. C. Greubel, Feb 21 2018 CROSSREFS Cf. A006720, A006721, A006722, A048736. Cf. A078495. Sequence in context: A003217 A297011 A178717 * A217097 A298590 A262451 Adjacent sequences:  A006720 A006721 A006722 * A006724 A006725 A006726 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from James A. Sellers, Aug 22 2000 STATUS approved

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Last modified July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)