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%I #6 Dec 12 2014 21:00:33
%S 2,395,2048,9413,30848,84259,198570,421913,823336,1504241,2601366,
%T 4297747,6831608,10505741,15697544,22873679,32598374,45551245,
%U 62537376,84505589,112561702,147987947,192258132,247057213,314300264,396153407
%N Number of length 1+6 0..n arrays with every seven consecutive terms having six times some element equal to the sum of the remaining six
%C Row 1 of A249359
%H R. H. Hardin, <a href="/A249360/b249360.txt">Table of n, a(n) for n = 1..54</a>
%F Empirical: a(n) = 5*a(n-1) -11*a(n-2) +15*a(n-3) -15*a(n-4) +12*a(n-5) -9*a(n-6) +7*a(n-7) -4*a(n-8) +4*a(n-10) -7*a(n-11) +9*a(n-12) -12*a(n-13) +15*a(n-14) -15*a(n-15) +11*a(n-16) -5*a(n-17) +a(n-18)
%F Also a polynomial of degree 6 plus a quasipolynomial of degree 0 with period 60, the first 12 being:
%F Empirical for n mod 60 = 0: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + 1
%F Empirical for n mod 60 = 1: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (983/60)
%F Empirical for n mod 60 = 2: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (467/5)
%F Empirical for n mod 60 = 3: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (1373/20)
%F Empirical for n mod 60 = 4: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (967/15)
%F Empirical for n mod 60 = 5: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (353/4)
%F Empirical for n mod 60 = 6: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (551/5)
%F Empirical for n mod 60 = 7: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (7871/60)
%F Empirical for n mod 60 = 8: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (1013/5)
%F Empirical for n mod 60 = 9: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (3109/20)
%F Empirical for n mod 60 = 10: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (143/3)
%F Empirical for n mod 60 = 11: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (1819/20)
%e Some solutions for n=6
%e ..3....0....3....2....0....2....4....6....1....2....2....4....4....6....5....6
%e ..3....2....5....6....0....4....0....6....6....3....0....3....2....6....5....3
%e ..4....0....4....0....6....5....6....6....0....4....3....3....5....4....3....0
%e ..4....4....1....0....3....5....6....1....2....1....3....6....5....5....3....4
%e ..5....3....0....0....3....3....6....4....2....5....5....3....2....1....6....3
%e ..3....5....4....2....0....6....2....3....2....3....6....2....6....2....4....3
%e ..6....0....4....4....2....3....4....2....1....3....2....0....4....4....2....2
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 26 2014
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