A112959 a(1) = a(2) = a(3) = a(4) = a(5) = 1; for n>1: a(n+5) = (a(n))^2 + (a(n+1))^2 + (a(n+2))^2 + (a(n+3))^2 + (a(n+4))^2.

1, 1, 1, 1, 1, 5, 29, 869, 756029, 571580604869, 326704387862983487112029, 106735757048926752040856495274871386126283608845

Offset

1,6

Comments

A quadratic pentanacci sequence.

This is to A000283 as a pentanacci (A000322) is to Fibonacci. Primes in this begin a(6) = 5 and a(7) = 29. a(8), a(9), a(10) and a(11) are semiprime.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..16

Example

5^2 + 29^2 + 869^2 + 756029^2 + 571580604869^2 = 326704387862983487112029.

Mathematica

RecurrenceTable[{a[1] == a[2] == a[3] == a[4] == a[5] == 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, 16}] (* Vincenzo Librandi, Aug 21 2016 *)

Crossrefs

Cf. A000283, A000288, A112957, A112958, A112960.

Sequence in context: A144994 A263369 A072880 * A273918 A085553 A057208

Adjacent sequences: A112956 A112957 A112958 * A112960 A112961 A112962

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 02 2006

Status

approved