A058232 a(n) = (a(n-1)a(n-5) + a(n-2)a(n-4) + a(n-3)^2)/a(n-6).

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, -9, 8, 15, -4, 17, -8, -23, -3, -21, -49, 52, 76, -47, 11, -133, 79, 238, 97, 518, -417, -750, 625, -647, -343, 1967, 3048, -1000, 5553, -8375, -4233, 13375, 10912, 33503

Offset: 0

Author

Michael Somos, Dec 01 2000

Keywords

• sign
• easy
• nice

Comments

Satisfies the defining recursion for the Somos-6 sequence. - Michael Somos, May 25 2014

References

• N. D. Elkies, email, Nov 29 2000.

Links

• T. D. Noe, Table of n, a(n) for n=0..300
• Index entries for two-way infinite sequences

Crossrefs

Cf. A006722.

Programs

Mathematica

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 *)

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]))};

Formula

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.

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

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

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