A362884 a(n) = (a(n-1)*a(n-2)*a(n-3)+64)/(4*a(n-4)) with a(0) = a(2) = a(3) = 2 and a(1) = 16.

2, 16, 2, 2, 16, 2, 16, 72, 37, 5336, 222112, 152263946, 1219335473828432, 1932041718420459629645062, 403742785702569426305018937234491996105486, 1561663327784579146423924791055619905538560428937482474084426146608982032

Offset

0,1

Comments

Conjecture 1: all terms are integer.

Conjecture 2: a(n) is never divisible by 64.

Links

Table of n, a(n) for n=0..15.

Formula

For n >= 2, a(n) = 4 * A276175(n) * A276175(n-2) / (A276175(n-1) * (A276175(n-1) + 1)).

Mathematica

nxt[{a_, b_, c_, d_}]:={b, c, d, (d*c*b+64)/(4a)}; NestList[nxt, {2, 16, 2, 2}, 20][[;; , 1]] (* Harvey P. Dale, Nov 25 2025 *)

Crossrefs

Cf. A276175.

Sequence in context: A221076 A230513 A300138 * A217028 A145684 A254637

Adjacent sequences: A362881 A362882 A362883 * A362885 A362886 A362887

Keyword

nonn

Author

Max Alekseyev, May 07 2023

Status

approved