A253394 Number of (n+1) X (5+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

304, 250, 316, 465, 666, 932, 1269, 1693, 2201, 2814, 3527, 4360, 5309, 6394, 7611, 8980, 10497, 12182, 14031, 16064, 18277, 20690, 23299, 26124, 29161, 32430, 35927, 39672, 43661, 47914, 52427, 57220, 62289, 67654, 73311, 79280, 85557, 92162, 99091

Offset: 1

Author

R. H. Hardin, Dec 31 2014

Keywords

• nonn

Examples

			Some solutions for n=4:
..0..0..0..0..0..1....0..0..0..0..1..1....1..1..1..1..1..1....1..1..0..1..0..1
..0..0..0..0..0..0....0..0..0..0..0..0....1..1..1..1..0..0....1..1..0..1..0..1
..0..0..0..0..0..0....0..0..0..0..0..1....1..1..1..1..1..1....1..1..0..1..0..1
..0..0..0..0..1..0....0..0..0..0..0..1....1..1..0..0..0..0....1..1..0..1..0..1
..1..1..1..0..1..0....1..1..1..1..0..1....1..1..1..1..1..1....1..1..0..1..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Column 5 of A253397.

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) for n>13.

Empirical for n mod 2 = 0: a(n) = (4/3)*n^3 + 13*n^2 + (5/3)*n + 164 for n>8.

Empirical for n mod 2 = 1: a(n) = (4/3)*n^3 + 13*n^2 + (5/3)*n + 161 for n>8.

Empirical g.f.: x*(304 - 662*x + 174*x^2 + 625*x^3 - 509*x^4 + 50*x^5 + 37*x^6 + 3*x^7 - 9*x^8 + 5*x^9 - 2*x^10 - x^11 + x^12) / ((1 - x)^4*(1 + x)). - Colin Barker, Dec 12 2018