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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.

%I A112960 #16 Apr 12 2020 12:22:02
%S A112960 1,1,1,1,1,1,6,41,1721,2963561,8782696764281,
%T A112960 77135762453320729974211241,
%U A112960 5949925849255124079413733148488788342637650064971321
%N 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.
%C A112960 A quadratic hexanacci sequence.
%C A112960 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).
%H A112960 Seiichi Manyama, <a href="/A112960/b112960.txt">Table of n, a(n) for n = 1..17</a>
%e A112960 1^2 + 6^2 + 41^2 + 1721^2 + 2963561^2 + 8782696764281^2 = 77135762453320729974211241.
%t A112960 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 *)
%t A112960 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 *)
%Y A112960 Cf. A000283, A000383, A112957, A112958, A112959.
%K A112960 easy,nonn
%O A112960 1,7
%A A112960 _Jonathan Vos Post_, Jan 02 2006