A112960 a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = 1; for n>1: a(n+6) = (a(n))^2 + (a(n+1))^2 + (a(n+2))^2 + (a(n+3))^2 + (a(n+4))^2 + (a(n+5))^2.

1, 1, 1, 1, 1, 1, 6, 41, 1721, 2963561, 8782696764281, 77135762453320729974211241, 5949925849255124079413733148488788342637650064971321

Offset

1,7

Comments

A quadratic hexanacci sequence.

This is to A000283 as a hexanacci (A000383) is to Fibonacci. Primes in this begin a(8) = 41, a(9) = 1721. Semiprimes begin a(7), a(10), a(12).

Links

Seiichi Manyama, Table of n, a(n) for n = 1..17

Example

1^2 + 6^2 + 41^2 + 1721^2 + 2963561^2 + 8782696764281^2 = 77135762453320729974211241.

Mathematica

RecurrenceTable[{a[1] == a[2] == a[3] == a[4] == a[5] == a[6] == 1, a[n] == a[n-1]^2 + a[n-2]^2 + a[n-3]^2 + a[n-4]^2 + a[n-5]^2 + a[n-6]^2}, a, {n, 17}] (* Vincenzo Librandi, Aug 21 2016 *)
nxt[{a_, b_, c_, d_, e_, f_}]:={b, c, d, e, f, a^2+b^2+c^2+d^2+e^2+f^2}; NestList[ nxt, {1, 1, 1, 1, 1, 1}, 12][[All, 1]] (* Harvey P. Dale, Apr 12 2020 *)

Crossrefs

Cf. A000283, A000383, A112957, A112958, A112959.

Sequence in context: A230134 A007130 A075000 * A181041 A109856 A249135

Adjacent sequences: A112957 A112958 A112959 * A112961 A112962 A112963

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 02 2006

Status

approved