A253228 - OEIS

%I #7 Dec 10 2018 12:18:47

%S 907,1775,1709,2543,3936,6414,11022,19851,37083,71082,138576,273021,

%T 541329,1077324,2148654,4290615,8573799,17139390,34269756,68529633,

%U 137048493,274085280,548157882,1096302075,2192589411,4385162994

%N Number of (n+1) X (5+1) 0..1 arrays with every 2 X 2 subblock diagonal minimum minus antidiagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal maximum nondecreasing vertically.

%H R. H. Hardin, <a href="/A253228/b253228.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>8.

%F Conjectures from _Colin Barker_, Dec 10 2018: (Start)

%F G.f.: x*(907 - 2760*x + 997*x^2 + 3624*x^3 - 4009*x^4 + 1208*x^5 - 7*x^6 + x^7) / ((1 - x)^3*(1 - 2*x)).

%F a(n) = (3/32)*(5280 + 697*2^n + 1840*n + 208*n^2) for n>4.

%F (End)

%e Some solutions for n=4:

%e ..0..1..0..1..0..0....1..1..1..1..1..1....0..1..1..1..1..1....1..1..0..0..1..1

%e ..0..1..0..1..0..0....1..1..1..1..1..1....0..0..0..0..0..0....1..1..0..0..0..0

%e ..0..1..0..1..0..0....1..1..1..1..1..1....1..0..0..0..0..0....1..1..0..0..0..0

%e ..1..1..0..1..0..0....1..1..1..1..1..1....1..0..0..0..0..0....0..0..0..0..0..0

%e ..1..0..0..1..0..1....0..0..0..0..0..1....0..0..0..0..0..0....0..0..1..1..1..1

%Y Column 5 of A253231.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 29 2014