|
%I #19 Feb 16 2015 14:35:02
%S 0,1,0,1,1,-1,-1,0,0,1,-1,-1,-1,-2,1,2,-1,2,1,-3,-3,-1,-4,4,1,-3,-5,
%T -9,8,15,-4,17,-8,-23,-3,-21,-49,52,76,-47,11,-133,79,238,97,518,-417,
%U -750,625,-647,-343,1967,3048,-1000,5553,-8375,-4233,13375,10912,33503
%N a(n) = (a(n-1)a(n-5) + a(n-2)a(n-4) + a(n-3)^2)/a(n-6).
%C Satisfies the defining recursion for the Somos-6 sequence. - _Michael Somos_, May 25 2014
%D N. D. Elkies, email, Nov 29 2000.
%H T. D. Noe, <a href="/A058232/b058232.txt">Table of n, a(n) for n=0..300</a>
%H <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%F a(-n) = -a(n). a(n+6) * a(n-6) = a(n+4) * a(n-4) + a(n+2) * a(n-2) for all n in Z.
%F a(n+6) * a(n-6) = -a(n+5) * a(n-5) + 2*a(n+4) * a(n-4) - a(n)^2 for all n in Z. - _Michael Somos_, May 25 2014
%F a(n+6) * a(n-5) = - a(n+4) * a(n-3) + a(n+2) * a(n-1) for all n in Z. - _Michael Somos_, May 25 2014
%F a(n+5) * a(n-4) = a(n+4) * a(n-3) + a(n+3) * a(n-2) - a(n+2) * a(n-1) + a(n+1) * a(n) for all n in Z. - _Michael Somos_, May 25 2014
%t nxt[{a_,b_,c_,d_,e_,f_}]:={b,c,d,e,f,(f*b+e*c+d^2)/a}; Join[ {0,1,0,1,1,-1,-1,0,0}, Transpose[ NestList[ nxt,{1,-1,-1,-1,-2,1},50]][[1]]] (* _Harvey P. Dale_, Apr 06 2013 *)
%o (PARI) {a(n) = local(an, a0, num); if( n<0, -a(-n), if( n==0, 0, a0 = [1, 0, 1, 1, -1, -1, 0, 0, 1, -1, -1, -1, -2, 1]; an = vector(n); for( k=1, n, an[k] = if( k<15, a0[k], (num = an[k-1] * an[k-5] + an[k-2] * an[k-4] + an[k-3]^2) / an[k-6])); an[n]))};
%Y Cf. A006722.
%K sign,easy,nice
%O 0,14
%A _Michael Somos_, Dec 01 2000
|
