A241593 a(0)-a(5) are -1, 0, 1, 12, -432, 93312; thereafter a(n) = (144*a(n-3)*a(n-1)+432*a(n-2)^2)/a(n-4).

-1, 0, 1, 12, -432, 93312, 241864704, -940369969152, -29249267520503808, -6823269127183128330240, 5348220265883981394311380992, 2566558951457996941025058427502592, -336245011425341849227546073789919098044416

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..54

R. W. Gosper and Richard C. Schroeppel, Somos Sequence Near-Addition Formulas and Modular Theta Functions, arXiv:math/0703470 [math.NT], 2007. See p. 18.

Maple

f:=proc(n) option remember;
if n <= 2 then n-1
elif n=3 then 12
elif n=4 then -432
elif n=5 then 93312
else (144*f(n-3)*f(n-1)+432*f(n-2)^2)/f(n-4); fi; end;
(144*a(n-3)*a(n-1)+432*a(n-2)^2)/a(n-4); ai; end;
[seq(f(n), n=0..15)];

Mathematica

a[n_] := a[n] = Which[n <= 2, n - 1, n == 3, 12, n == 4, -432, n == 5, 93312, True, (144*a[n - 3]*a[n - 1] + 432 a[n - 2]^2)/a[n - 4]];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Dec 05 2017 *)
nxt[{a_, b_, c_, d_}]:={b, c, d, (144b*d+432c^2)/a}; Join[{-1, 0}, NestList[nxt, {1, 12, -432, 93312}, 10][[All, 1]]] (* Harvey P. Dale, Dec 30 2017 *)

Prog

(Magma) I:=[1, 12, -432, 93312]; [-1, 0] cat [n le 4 select I[n] else (144*Self(n-3)*Self(n-1) + 432*Self(n - 2)^2)/Self(n-4): n in [1..20]]; // G. C. Greubel, Aug 08 2018

Crossrefs

Sequence in context: A054913 A221955 A070285 * A041617 A159534 A303922

Adjacent sequences: A241590 A241591 A241592 * A241594 A241595 A241596

Keyword

sign

Author

N. J. A. Sloane, May 16 2014

Status

approved