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%I #6 Dec 12 2014 20:59:13
%S 2,15,52,113,246,427,704,1113,1654,2279,3072,4045,5210,6555,8116,9953,
%T 12054,14383,16976,19929,23194,26735,30636,34993,39686,44751,50212,
%U 56201,62646,69451,76712,84609,93010,101879,111252,121321,131942,143103,154840
%N Number of length 2+3 0..n arrays with every four consecutive terms having the sum of some three elements equal to three times the fourth
%C Row 2 of A248537
%H R. H. Hardin, <a href="/A248539/b248539.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) -a(n-2) +a(n-4) +a(n-7) +a(n-8) -a(n-9) +a(n-10) -a(n-12) -a(n-13) -a(n-15) -a(n-16) +a(n-18) -a(n-19) +a(n-20) +a(n-21) +a(n-24) -a(n-26) +a(n-27) -a(n-28)
%F Empirical also a cubic polynomial plus a linear quasipolynomial with period 360, the first 12 being:
%F Empirical for n mod 360 = 0: a(n) = (11/4)*n^3 - (113/20)*n^2 + (97/10)*n + 1
%F Empirical for n mod 360 = 1: a(n) = (11/4)*n^3 - (113/20)*n^2 + (209/20)*n - (111/20)
%F Empirical for n mod 360 = 2: a(n) = (11/4)*n^3 - (113/20)*n^2 + (97/10)*n - (19/5)
%F Empirical for n mod 360 = 3: a(n) = (11/4)*n^3 - (113/20)*n^2 + (149/20)*n + (25/4)
%F Empirical for n mod 360 = 4: a(n) = (11/4)*n^3 - (113/20)*n^2 + (97/10)*n - (57/5)
%F Empirical for n mod 360 = 5: a(n) = (11/4)*n^3 - (113/20)*n^2 + (209/20)*n - (35/4)
%F Empirical for n mod 360 = 6: a(n) = (11/4)*n^3 - (113/20)*n^2 + (97/10)*n - (109/5)
%F Empirical for n mod 360 = 7: a(n) = (11/4)*n^3 - (113/20)*n^2 + (149/20)*n - (291/20)
%F Empirical for n mod 360 = 8: a(n) = (11/4)*n^3 - (113/20)*n^2 + (97/10)*n - 11
%F Empirical for n mod 360 = 9: a(n) = (11/4)*n^3 - (113/20)*n^2 + (209/20)*n + (257/20)
%F Empirical for n mod 360 = 10: a(n) = (11/4)*n^3 - (113/20)*n^2 + (97/10)*n - 3
%F Empirical for n mod 360 = 11: a(n) = (11/4)*n^3 - (113/20)*n^2 + (149/20)*n + (269/20)
%e Some solutions for n=6
%e ..0....3....5....2....2....2....5....0....0....6....6....1....2....4....6....0
%e ..1....5....6....3....2....2....4....6....3....1....0....5....3....5....2....6
%e ..2....4....5....1....4....3....3....6....2....4....0....6....6....5....4....3
%e ..1....0....4....6....0....5....4....4....3....5....2....4....1....6....4....3
%e ..4....3....1....2....2....2....5....0....0....6....6....5....2....4....6....0
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 08 2014
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