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%I #7 Aug 18 2014 18:32:05
%S 0,1,1,1,1,4,13,121,8401,17724001,19980403610080,
%T 3017939125082738100693961,
%U 1069257489122187637992525695378883464262898201
%N a(n) = sum_{j=1..4} product_{k=1..4, k<>j} a(n-k).
%F a(n) = a(n-4)*a(n-3)*a(n-2) + a(n-4)*a(n-3)*a(n-1) + a(n-4)*a(n-2)*a(n-1) + a(n-3)*a(n-2)*a(n-1).
%e a(8) = a(4)*a(5)*a(6)+a(4)*a(5)*a(7)+a(4)*a(6)*a(7)+a(5)*a(6)*a(7) = 1*1*4 +1*1*13 +1*4*13 +1*4*13 = 121.
%t a[0] = 0; a[1] = 1; a[2] = 1; a[3] = 1; a[n_] : a[n] = a[ -4 + n] a[ -3 + n] a[ -2 + n] + a[ -4 + n] a[ -3 + n] a[ -1 + n] + a[ -4 + n] a[ -2 + n] a[ -1 + n] + a[ -3 + n] a[ -2 + n] a[ -1 + n] b = Table[a[n], {n, 0, 15}]
%t RecurrenceTable[{a[0]==0,a[1]==a[2]==a[3]==1,a[n]==a[n-4]a[n-3]a[n-2]+a[n-4]a[n-3]a[n-1]+a[n-4]a[n-2]a[n-1]+a[n-3]a[n-2]a[n-1]},a,{n,15}] (* _Harvey P. Dale_, Aug 18 2014 *)
%K nonn,easy
%O 1,6
%A _Roger L. Bagula_, Aug 30 2006
%E Explicit definition provided by the Assoc. Eds. of the OEIS - Mar 27 2010
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