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 A199901 Number of -n..n arrays x(0..5) of 6 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative. 1

%I

%S 75,533,2035,5725,13363,27457,51395,89577,147547,232125,351539,515557,

%T 735619,1024969,1398787,1874321,2471019,3210661,4117491,5218349,

%U 6542803,8123281,9995203,12197113,14770811,17761485,21217843,25192245,29740835

%N Number of -n..n arrays x(0..5) of 6 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.

%C Row 6 of A199898.

%H R. H. Hardin, <a href="/A199901/b199901.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (11/10)*n^5 + (55/6)*n^4 + (55/2)*n^3 + (173/6)*n^2 + (37/5)*n + 1.

%F Conjectures from _Colin Barker_, May 16 2018: (Start)

%F G.f.: x*(75 + 83*x - 38*x^2 + 10*x^3 + 3*x^4 - x^5) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

%F (End)

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Cf. A199898.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 11 2011

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Last modified March 31 11:51 EDT 2023. Contains 361648 sequences. (Running on oeis4.)