A241594 a(n) = -(8*a(n-4)*a(n-1)+57*a(n-3)*a(n-2))/a(n-5) with initial values 1, 0, -1, 1, 8, 57, -455.

1, 0, -1, 1, 8, 57, -455, 22352, 47767, 69739671, 3385862936, 1747973613295, -632038062613231, 319807929289790304, 778756000716629557903, 186509371006506937278833, -7581885296067966478838810840, -17592286469464275110206466526327, 594744699237794019378328459208828297

Offset: 0

Author

N. J. A. Sloane, May 18 2014

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..90
• R. W. Gosper and Richard C. Schroeppel, Somos Sequence Near-Addition Formulas and Modular Theta Functions, arXiv:math/0703470 [math.NT], 2007. See h_n.

Crossrefs

See A241595 for another version.

Cf. A360381.

Programs

Magma

I:=[22352, 47767, 69739671, 3385862936, 1747973613295]; [1, 0, -1, 1, 8, 57, -455] cat [n le 5 select I[n] else -(8*Self(n-4)*Self(n-1) + 57*Self(n-3)*Self(n-2))/Self(n-5): n in [1..20]]; // G. C. Greubel, Aug 08 2018

Maple

f:=proc(n) option remember;
if n <= 2 then 1-n
elif n=3 then 1
elif n=4 then 8
elif n=5 then 57
elif n=6 then -455
else -(8*f(n-4)*f(n-1)+57*f(n-3)*f(n-2))/f(n-5); fi; end;
[seq(f(n),n=0..30)];

Mathematica

a[n_] := a[n] = If[n <= 6, {1, 0, -1, 1, 8, 57, -455}[[n + 1]], -(8*a[n - 4]*a[n - 1] + 57*a[n - 3]*a[n - 2])/a[n - 5]];
Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Dec 02 2017 *)
nxt[{a_,b_,c_,d_,e_}]:={b,c,d,e,-(8b e+57c d)/a}; Join[{1,0},NestList[nxt,{-1,1,8,57,-455},20] [[;;,1]]] (* Harvey P. Dale, Aug 14 2023 *)

PARI

{a(n) = my(E = ellinit([1, 1, 0, -2, 0])); n--; subst(elldivpol(E, n), 'x, 1) * (-1)^(n%4!=2)}; /* Michael Somos, Mar 01 2025 */

PARI

{a(n) = my(E = ellinit([1, 1, 0, -2, 0])); n--; subst(elldivpol(E, 2*n), 'x, 2) * (-1)^(n + (n%4==2))/6^(n^2 + 1)}; /* Michael Somos, Mar 02 2025 */

Formula

-a(n+1) = A360381(2*n)*(-1)^(n%4!=0). a(n+2)*a(n-2) = -(-1)^n*a(n+1)*a(n-1) + 8*a(n)^2 for all n in Z. - Michael Somos, Mar 01 2025