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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.
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%I #15 Aug 21 2016 04:08:21

%S 1,1,1,1,1,5,29,869,756029,571580604869,326704387862983487112029,

%T 106735757048926752040856495274871386126283608845

%N 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.

%C A quadratic pentanacci sequence.

%C 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.

%H Seiichi Manyama, <a href="/A112959/b112959.txt">Table of n, a(n) for n = 1..16</a>

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

%t 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 *)

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

%K easy,nonn

%O 1,6

%A _Jonathan Vos Post_, Jan 02 2006