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 A246481 Number of length 2+3 0..n arrays with no pair in any consecutive four terms totalling exactly n. 1

%I #7 Nov 06 2018 06:44:59

%S 2,14,132,484,1734,4386,10376,20840,39690,68950,115212,181644,278222,

%T 409514,589584,824656,1133586,1524510,2021780,2635700,3396822,4317874,

%U 5436312,6767544,8356634,10221926,12416796,14962780,17922270,21320250

%N Number of length 2+3 0..n arrays with no pair in any consecutive four terms totalling exactly n.

%H R. H. Hardin, <a href="/A246481/b246481.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 8*a(n-3) + 6*a(n-4) + 6*a(n-5) - 8*a(n-6) + 3*a(n-8) - a(n-9).

%F Conjectures from _Colin Barker_, Nov 06 2018: (Start)

%F G.f.: 2*x*(1 + 4*x + 45*x^2 + 52*x^3 + 191*x^4 + 72*x^5 + 115*x^6) / ((1 - x)^6*(1 + x)^3).

%F a(n) = 5*n - 11*n^2 + 10*n^3 - 4*n^4 + n^5 for n even.

%F a(n) = 9 - 10*n - 4*n^2 + 10*n^3 - 4*n^4 + n^5 for n odd.

%F (End)

%e Some solutions for n=6:

%e ..0....1....0....0....3....3....3....4....6....6....5....2....4....1....2....0

%e ..2....0....0....5....6....1....2....3....3....1....0....0....0....1....5....4

%e ..0....4....0....4....6....4....6....4....4....3....5....0....5....2....6....1

%e ..2....4....3....5....6....6....2....4....4....6....0....0....3....0....6....4

%e ..0....1....2....0....1....6....3....6....0....2....4....0....5....2....6....1

%Y Row 2 of A246479.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 27 2014

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Last modified April 20 02:14 EDT 2024. Contains 371798 sequences. (Running on oeis4.)