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%I #4 Sep 28 2014 22:46:40
%S 32,702,5316,27800,104620,329742,884032,2131356,4664480,9508130,
%T 18168932,33008212,57264516,95672090,154419880,242095992,369529512,
%U 551174206,804749300,1153181480,1623975972,2251830342,3077638456,4151941100
%N Number of length 2+5 0..n arrays with no disjoint triples in any consecutive six terms having the same sum
%C Row 2 of A247995
%H R. H. Hardin, <a href="/A247997/b247997.txt">Table of n, a(n) for n = 1..45</a>
%F Empirical: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3) -3*a(n-4) +7*a(n-6) +4*a(n-7) -5*a(n-8) -4*a(n-9) -5*a(n-10) +4*a(n-11) +7*a(n-12) -3*a(n-14) -4*a(n-15) +2*a(n-16) +2*a(n-17) -a(n-18)
%F Empirical for n mod 12 = 0: a(n) = n^7 - 4*n^6 + (1523/32)*n^5 - (5325/32)*n^4 + (4180/9)*n^3 - (12625/24)*n^2 + (641/6)*n
%F Empirical for n mod 12 = 1: a(n) = n^7 - 4*n^6 + (1523/32)*n^5 - (5325/32)*n^4 + (64225/144)*n^3 - (20525/48)*n^2 - (24079/96)*n + (111235/288)
%F Empirical for n mod 12 = 2: a(n) = n^7 - 4*n^6 + (1523/32)*n^5 - (5325/32)*n^4 + (4180/9)*n^3 - (12625/24)*n^2 + (107/2)*n + (2260/9)
%F Empirical for n mod 12 = 3: a(n) = n^7 - 4*n^6 + (1523/32)*n^5 - (5325/32)*n^4 + (64225/144)*n^3 - (20525/48)*n^2 - (24079/96)*n + (16555/32)
%F Empirical for n mod 12 = 4: a(n) = n^7 - 4*n^6 + (1523/32)*n^5 - (5325/32)*n^4 + (4180/9)*n^3 - (12625/24)*n^2 + (641/6)*n - (640/9)
%F Empirical for n mod 12 = 5: a(n) = n^7 - 4*n^6 + (1523/32)*n^5 - (5325/32)*n^4 + (64225/144)*n^3 - (20525/48)*n^2 - (9733/32)*n + (209795/288)
%F Empirical for n mod 12 = 6: a(n) = n^7 - 4*n^6 + (1523/32)*n^5 - (5325/32)*n^4 + (4180/9)*n^3 - (12625/24)*n^2 + (641/6)*n - 20
%F Empirical for n mod 12 = 7: a(n) = n^7 - 4*n^6 + (1523/32)*n^5 - (5325/32)*n^4 + (64225/144)*n^3 - (20525/48)*n^2 - (24079/96)*n + (128515/288)
%F Empirical for n mod 12 = 8: a(n) = n^7 - 4*n^6 + (1523/32)*n^5 - (5325/32)*n^4 + (4180/9)*n^3 - (12625/24)*n^2 + (107/2)*n + (2440/9)
%F Empirical for n mod 12 = 9: a(n) = n^7 - 4*n^6 + (1523/32)*n^5 - (5325/32)*n^4 + (64225/144)*n^3 - (20525/48)*n^2 - (24079/96)*n + (14635/32)
%F Empirical for n mod 12 = 10: a(n) = n^7 - 4*n^6 + (1523/32)*n^5 - (5325/32)*n^4 + (4180/9)*n^3 - (12625/24)*n^2 + (641/6)*n - (820/9)
%F Empirical for n mod 12 = 11: a(n) = n^7 - 4*n^6 + (1523/32)*n^5 - (5325/32)*n^4 + (64225/144)*n^3 - (20525/48)*n^2 - (9733/32)*n + (227075/288)
%e Some solutions for n=5
%e ..4....0....4....5....2....5....5....2....3....2....1....3....1....3....3....2
%e ..1....5....5....4....0....1....3....2....2....0....1....4....2....1....5....3
%e ..1....4....5....2....1....4....0....4....1....0....4....3....0....5....5....2
%e ..5....0....0....1....5....2....0....3....3....1....5....5....3....3....2....3
%e ..2....3....5....5....1....0....3....1....1....1....0....3....2....4....4....0
%e ..4....5....3....0....2....3....4....1....3....1....0....5....5....1....2....1
%e ..2....0....0....3....4....5....3....2....3....2....4....1....0....1....3....0
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 28 2014
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