A112957 a(1) = a(2) = a(3) = 1; for n > 1, a(n+3) = a(n)^2 + a(n+1)^2 + a(n+2)^2.

1, 1, 1, 3, 11, 131, 17291, 298995963, 89398586189293211, 7992107212644486930829797919966571, 63873777698404030240264509605345282496735163325301838600463378485931

Offset

1,4

Comments

A quadratic tribonacci sequence.

This is to A000283 as a tribonacci (A000213) is to Fibonacci. Two oddities about this sequence: (a) its first 7 terms are identical to terms numbered 2 through 8 of A072878; (b) only one of the first 9 terms are composite. Primes in the sequence begin 3, 11, 131, 17291 and 89398586189293211. What is the next prime?

Links

Seiichi Manyama, Table of n, a(n) for n = 1..14

Mathematica

Join[{a=1, b=1, c=1}, Table[d=a*a+b*b+c*c; a=b; b=c; c=d, {n, 10}]] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *)

Crossrefs

Cf. A000213, A000283, A072878, A112958, A112959, A112960.

Sequence in context: A276258 A284604 A072878 * A057205 A121897 A067657

Adjacent sequences: A112954 A112955 A112956 * A112958 A112959 A112960

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 02 2006; definition corrected Jan 02 2006

Status

approved