A276257 a(1) = a(2) = a(3) = a(4) = 1; for n>4, a(n) = ( a(n-1)+a(n-2)+a(n-3)+1 )^2 / a(n-4).

1, 1, 1, 1, 16, 361, 143641, 20741472361, 26888415586959536281, 2002733778095476250641191709976062096, 27923382501685315585533445603599269911720565853675615809277429923281

Offset: 1

Author

Seiichi Manyama, Aug 25 2016

Keywords

• nonn

Comments

All terms are perfect squares.

The next term (a(12)) has 125 digits. - Harvey P. Dale, Jul 04 2019

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..15

Crossrefs

Cf. A276097, A276256, A276259.

Programs

Mathematica

RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1,a[n]==(a[n-1]+a[n-2]+ a[n-3]+ 1)^2/a[n-4]},a,{n,11}] (* Harvey P. Dale, Jul 04 2019 *)

Formula

a(n) = A276259(n)^2

a(n) = 25*a(n-1)*a(n-2)*a(n-3) - 2*a(n-1) - 2*a(n-2) - 2*a(n-3) - 2 - a(n-4).

a(n)*a(n-1)*a(n-2)*a(n-3) = ((a(n) + a(n-1) + a(n-2) + a(n-3) + 1)/5)^2.