|
%I #4 Sep 30 2014 21:56:13
%S 32,513,3364,15125,48316,131677,299968,625269,1174080,2085341,3462212,
%T 5539433,8458164,12578465,18080936,25484457,35000808,47350769,
%U 62767700,82210901,105929332,135165573,170162104,212500725,262397536,321818557
%N Number of length 2+5 0..n arrays with some disjoint triples in each consecutive six terms having the same sum
%C Row 2 of A248068
%H R. H. Hardin, <a href="/A248070/b248070.txt">Table of n, a(n) for n = 1..55</a>
%F Empirical: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) -6*a(n-5) -3*a(n-6) +4*a(n-7) +6*a(n-8) +4*a(n-9) -3*a(n-10) -6*a(n-11) -2*a(n-12) +2*a(n-13) +3*a(n-14) -a(n-16)
%F Empirical for n mod 12 = 0: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (4450/9)*n^3 - (13225/24)*n^2 + (467/6)*n + 1
%F Empirical for n mod 12 = 1: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (68545/144)*n^3 - (21725/48)*n^2 - (25423/96)*n + (115843/288)
%F Empirical for n mod 12 = 2: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (4450/9)*n^3 - (13225/24)*n^2 + (49/2)*n + (2269/9)
%F Empirical for n mod 12 = 3: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (68545/144)*n^3 - (21725/48)*n^2 - (25423/96)*n + (17067/32)
%F Empirical for n mod 12 = 4: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (4450/9)*n^3 - (13225/24)*n^2 + (467/6)*n - (631/9)
%F Empirical for n mod 12 = 5: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (68545/144)*n^3 - (21725/48)*n^2 - (10181/32)*n + (214403/288)
%F Empirical for n mod 12 = 6: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (4450/9)*n^3 - (13225/24)*n^2 + (467/6)*n - 19
%F Empirical for n mod 12 = 7: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (68545/144)*n^3 - (21725/48)*n^2 - (25423/96)*n + (133123/288)
%F Empirical for n mod 12 = 8: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (4450/9)*n^3 - (13225/24)*n^2 + (49/2)*n + (2449/9)
%F Empirical for n mod 12 = 9: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (68545/144)*n^3 - (21725/48)*n^2 - (25423/96)*n + (15147/32)
%F Empirical for n mod 12 = 10: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (4450/9)*n^3 - (13225/24)*n^2 + (467/6)*n - (811/9)
%F Empirical for n mod 12 = 11: a(n) = (1043/32)*n^5 - (5165/32)*n^4 + (68545/144)*n^3 - (21725/48)*n^2 - (10181/32)*n + (231683/288)
%e Some solutions for n=6
%e ..4....0....4....4....4....3....0....0....4....0....3....4....2....4....4....1
%e ..3....1....5....2....4....2....6....3....3....1....1....3....2....4....5....3
%e ..5....6....4....1....5....4....3....3....4....0....1....0....2....3....3....4
%e ..3....4....0....2....3....4....0....5....2....0....5....6....1....2....2....0
%e ..4....2....2....1....5....5....5....5....4....4....2....5....2....6....4....2
%e ..3....5....5....0....3....2....4....4....3....3....4....6....3....1....4....0
%e ..2....4....6....4....6....5....0....0....0....2....3....2....0....0....2....1
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 30 2014
| 