A251936 - OEIS

%I #8 Dec 01 2018 04:40:13

%S 10,43,120,265,506,875,1408,2145,3130,4411,6040,8073,10570,13595,

%T 17216,21505,26538,32395,39160,46921,55770,65803,77120,89825,104026,

%U 119835,137368,156745,178090,201531,227200,255233,285770,318955,354936,393865

%N Number of length 2+2 0..n arrays with the sum of the maximum minus the median of adjacent triples multiplied by some arrangement of +-1 equal to zero.

%H R. H. Hardin, <a href="/A251936/b251936.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/6)*n^4 + (7/3)*n^3 + (23/6)*n^2 + (8/3)*n + 1.

%F Conjectures from _Colin Barker_, Dec 01 2018: (Start)

%F G.f.: x*(10 - 7*x + 5*x^2 - 5*x^3 + x^4) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=6:

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

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

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

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

%Y Row 2 of A251935.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 11 2014