Search: id:A006769
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%I A006769 M0157
%S A006769 0,1,1,1,1,2,1,3,5,7,4,23,29,59,129,314,65,1529,3689,8209,16264,83313,
%T A006769 113689,620297,2382785,7869898,7001471,126742987,398035821,1687054711,
%U A006769 7911171596,47301104551,43244638645,1123424582771,6480598259201
%V A006769 0,1,1,-1,1,2,-1,-3,-5,7,-4,-23,29,59,129,-314,-65,1529,-3689,-8209,
%W A006769 -16264,83313,113689,-620297,2382785,7869898,7001471,-126742987,
%X A006769 -398035821,1687054711,-7911171596,-47301104551,43244638645
%N A006769 Elliptic divisibility sequence associated with y^2-y=x^3-x and the point 
               (0,0).
%C A006769 A Somos-4 sequence.
%D A006769 G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence 
               Sequences, Amer. Math. Soc., 2003; pp. 11 and 164.
%D A006769 C. Kimberling, Strong divisibility sequences and some conjectures, Fib. 
               Quart., 17 (1979), 13-17.
%D A006769 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006769 T. D. Noe, <a href="b006769.txt">Table of n, a(n) for n=0..100</a>
%H A006769 H. W. Braden, V. Z. Enolskii and A. N. W. Hone, <a href="http://arXiv.org/
               abs/math.NT/0501162">Bilinear recurrences and addition formulae for 
               hyperelliptic sigma functions</a>
%H A006769 G. Everest, <a href="http://www.mth.uea.ac.uk/~h090/EDS.html">Elliptic 
               Divisibility Sequences</a>
%H A006769 M. Somos, <a href="http://grail.cba.csuohio.edu/~somos/nwic.html">Number 
               Walls in Combinatorics</a>
%H A006769 <a href="Sindx_Tu.html#2wis">Index entries for two-way infinite sequences</
               a>
%F A006769 a(n)=(a(n-1)a(n-3)+a(n-2)^2)/a(n-4).
%F A006769 a(2n+1)=a(n+2)a(n)^3 - a(n-1)a(n+1)^3, a(2n)=a(n+2)a(n)a(n-1)^2 - a(n)a(n-2)a(n+1)^2.
%o A006769 (PARI) a(n)=local(an);if(n<0,-a(-n),if(n==0,0,an=vector(max(3,n),i,1);
               an[3]=-1;for(k=5,n,an[k]=(an[k-1]*an[k-3]+an[k-2]^2)/an[k-4]);an[n]))
%o A006769 (PARI) a(n)=local(an);if(n<0,-a(-n),if(n==0,0,an=Vec((-1-2*x+sqrt(1+4*x-4*x^3+O(x^n)))/
               (2*x^2));matdet(matrix((n-1)\2,(n-1)\2,i,j,if(i+j-1-n%2<0,0,an[i+j-n%2])))))
%o A006769 (PARI) a(n)=local(E,z); E=ellinit([0,0,-1,-1,0]); z=ellpointtoz(E,[0,
               0]); round(ellsigma(E,n*z)/sqrt(-ellsigma(E,z)*ellsigma(E,3*z)/ellsigma(E,
               2*z)^2)^(n^2)) /* Michael Somos Oct 22 2004 */
%Y A006769 A006720(n)=(-1)^n*a(2n-3).
%Y A006769 Squared terms give A028941.
%Y A006769 Sequence in context: A161169 A058202 A127201 this_sequence A075643 A076074 
               A135017
%Y A006769 Adjacent sequences: A006766 A006767 A006768 this_sequence A006770 A006771 
               A006772
%K A006769 sign,easy,nice
%O A006769 0,6
%A A006769 Michael Somos

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