|
%I #7 Dec 17 2018 08:13:42
%S 884,1712,3052,5136,7948,11740,16592,22720,30300,39560,50740,64104,
%T 79936,98540,120240,145380,174324,207456,245180,287920,336120,390244,
%U 450776,518220,593100,675960,767364,867896,978160,1098780,1230400,1373684
%N Number of (n+2) X (5+2) 0..1 arrays with every 2 X 2 and 3 X 3 subblock diagonal maximum minus antidiagonal minimum nondecreasing horizontally and vertically.
%H R. H. Hardin, <a href="/A253507/b253507.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (5/6)*n^4 + 9*n^3 + (1135/6)*n^2 + 361*n - 300 for n>8.
%F Conjectures from _Colin Barker_, Dec 17 2018: (Start)
%F G.f.: 4*x*(221 - 677*x + 833*x^2 - 461*x^3 + 22*x^4 + 129*x^5 - 110*x^6 + 77*x^7 - 44*x^8 + 23*x^9 - 10*x^10 + 3*x^11 - x^12) / (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>13.
%F (End)
%e Some solutions for n=4:
%e ..1..1..1..1..1..1..1....0..1..1..1..1..1..1....0..1..1..1..1..1..1
%e ..1..1..1..1..1..1..1....1..1..1..1..1..1..1....1..1..1..1..0..0..0
%e ..1..1..1..1..1..1..1....1..1..1..1..1..0..1....1..1..1..1..1..1..1
%e ..1..1..1..1..1..1..0....1..1..1..1..1..0..1....1..1..1..0..0..0..0
%e ..1..1..1..1..1..1..1....1..1..1..1..1..0..1....1..1..1..1..1..1..1
%e ..1..1..1..0..0..0..0....0..0..0..0..1..0..1....1..1..0..0..0..0..0
%Y Column 5 of A253510.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 02 2015
| 