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%I #4 Dec 15 2014 07:10:10
%S 40,369,1872,6361,17092,39109,79672,148673,259248,428045,675436,
%T 1027273,1513112,2169245,3037220,4166229,5610160,7435141,9709732,
%U 12516761,15944392,20095193,25074784,31012613,38034620,46293613,55944576,67167485
%N Number of length 4+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero
%C Row 4 of A252177
%H R. H. Hardin, <a href="/A252180/b252180.txt">Table of n, a(n) for n = 1..94</a>
%F Empirical: a(n) = -a(n-1) +a(n-2) +5*a(n-3) +6*a(n-4) -2*a(n-5) -12*a(n-6) -16*a(n-7) -3*a(n-8) +17*a(n-9) +25*a(n-10) +13*a(n-11) -13*a(n-12) -25*a(n-13) -17*a(n-14) +3*a(n-15) +16*a(n-16) +12*a(n-17) +2*a(n-18) -6*a(n-19) -5*a(n-20) -a(n-21) +a(n-22) +a(n-23)
%F Empirical for n mod 12 = 0: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (12695/1296)*n^3 + (3389/360)*n^2 + (409/90)*n + 1
%F Empirical for n mod 12 = 1: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (6253/648)*n^3 + (132259/12960)*n^2 + (91631/12960)*n + (4645/5184)
%F Empirical for n mod 12 = 2: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (12631/1296)*n^3 + (30341/3240)*n^2 + (6647/1620)*n + (37/324)
%F Empirical for n mod 12 = 3: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (6253/648)*n^3 + (14411/1440)*n^2 + (10039/1440)*n + (69/64)
%F Empirical for n mod 12 = 4: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (12695/1296)*n^3 + (31141/3240)*n^2 + (3761/810)*n - (35/81)
%F Empirical for n mod 12 = 5: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (6221/648)*n^3 + (129059/12960)*n^2 + (81391/12960)*n + (6181/5184)
%F Empirical for n mod 12 = 6: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (12695/1296)*n^3 + (3389/360)*n^2 + (863/180)*n + (5/4)
%F Empirical for n mod 12 = 7: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (6253/648)*n^3 + (132259/12960)*n^2 + (91631/12960)*n - (1835/5184)
%F Empirical for n mod 12 = 8: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (12631/1296)*n^3 + (30341/3240)*n^2 + (3121/810)*n - (11/81)
%F Empirical for n mod 12 = 9: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (6253/648)*n^3 + (14411/1440)*n^2 + (10039/1440)*n + (149/64)
%F Empirical for n mod 12 = 10: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (12695/1296)*n^3 + (31141/3240)*n^2 + (7927/1620)*n - (59/324)
%F Empirical for n mod 12 = 11: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (6221/648)*n^3 + (129059/12960)*n^2 + (81391/12960)*n - (299/5184)
%e Some solutions for n=6
%e ..6....3....4....1....6....2....0....5....1....2....4....1....3....0....3....4
%e ..6....0....5....3....4....3....3....4....3....1....4....3....4....2....3....2
%e ..2....6....2....1....2....3....5....0....1....3....1....6....1....5....4....6
%e ..0....3....5....5....0....2....1....6....2....3....3....1....2....3....1....2
%e ..5....6....5....3....5....1....4....6....0....1....4....6....4....1....0....0
%e ..3....6....2....3....1....3....3....1....6....1....1....3....5....3....2....0
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 15 2014
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