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%I #4 Oct 30 2014 14:19:53
%S 2,123,604,2045,5706,13087,26948,50529,88510,146351,231312,351913,
%T 518234,742275,1038016,1421237,1910418,2525719,3290420,4230141,
%U 5373382,6751463,8398944,10353505,12656246,15351627,18488128,22117469,26295930,31083331
%N Number of length 1+5 0..n arrays with every six consecutive terms having five times some element equal to the sum of the remaining five
%C Row 1 of A249497
%H R. H. Hardin, <a href="/A249498/b249498.txt">Table of n, a(n) for n = 1..111</a>
%F Empirical: a(n) = 3*a(n-1) -3*a(n-2) +2*a(n-3) -2*a(n-4) +a(n-5) -a(n-6) +a(n-7) +a(n-8) -a(n-9) +a(n-10) -2*a(n-11) +2*a(n-12) -3*a(n-13) +3*a(n-14) -a(n-15)
%F Empirical for n mod 60 = 0: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n + 1
%F Empirical for n mod 60 = 1: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n - (487/60)
%F Empirical for n mod 60 = 2: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n + (139/15)
%F Empirical for n mod 60 = 3: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n + (203/20)
%F Empirical for n mod 60 = 4: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n - (457/15)
%F Empirical for n mod 60 = 5: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n + (437/12)
%F Empirical for n mod 60 = 6: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n - (151/5)
%F Empirical for n mod 60 = 7: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n + (881/60)
%F Empirical for n mod 60 = 8: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n - (329/15)
%F Empirical for n mod 60 = 9: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n + (899/20)
%F Empirical for n mod 60 = 10: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n - (77/3)
%F Empirical for n mod 60 = 11: a(n) = (6/5)*n^5 + (9/4)*n^4 + (11/3)*n^3 + 2*n^2 + n - (1487/60)
%e Some solutions for n=6
%e ..1....1....4....4....3....1....0....6....4....2....2....5....2....5....6....3
%e ..4....4....6....5....4....6....3....3....5....0....2....2....2....4....4....4
%e ..3....5....0....3....6....6....1....6....5....0....3....1....0....3....5....5
%e ..3....6....3....4....0....1....1....2....6....6....4....4....5....0....3....1
%e ..3....4....4....1....3....4....1....0....5....2....2....6....6....5....6....6
%e ..4....4....1....1....2....6....0....1....5....2....5....6....3....1....6....5
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 30 2014
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