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a(n-1)*a(n-6) + a(n-2)*a(n-7) + a(n-3)*a(n-8) + a(n-4)*a(n-9), with a(k<8) = 1.
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%I #11 Jul 11 2015 11:13:11

%S 1,1,1,1,1,1,1,1,4,7,13,25,49,94,463,3691,51649,1342825,67140874,

%T 6378379789,2959568174113,10926725697533971,564365382277563803725,

%U 757844508822251885989584694,50882343436271211095738004051924943

%N a(n-1)*a(n-6) + a(n-2)*a(n-7) + a(n-3)*a(n-8) + a(n-4)*a(n-9), with a(k<8) = 1.

%C This is the 4-term analog of the 2-term recurrence A111288 a(1) = a(2) = a(3) = a(4) = 1. For n>= 5, a(n) = a(n-1)*a(n-3) + a(n-2)*a(n-4). Primes in this sequence include a(n) for n = 9, 10, 14, 15... with a(16) through a(28) composite, a(28) has 74 digits and the sequence growing beyond my ability to efficiently test primality.

%H Harvey P. Dale, <a href="/A118334/b118334.txt">Table of n, a(n) for n = 0..37</a>

%F a(0) = a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = a(7) = 1; for n>7: a(n) = a(n-1)*a(n-6) + a(n-2)*a(n-7) + a(n-3)*a(n-8) + a(n-4)*a(n-9).

%t nxt[{a_,b_,c_,d_,e_,f_,g_,h_,i_}]:={b,c,d,e,f,g,h,i,Total[ {a*f+ b*g+ c*h+ d*i}]}; Transpose[NestList[nxt,{1,1,1,1,1,1,1,1,1},30]][[1]] (* _Harvey P. Dale_, Aug 21 2014 *)

%Y Cf. A111288, A111388.

%K easy,nonn

%O 0,9

%A _Jonathan Vos Post_, May 14 2006