A184547 Number of (n+2) X 10 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

682, 2000, 4837, 10909, 23648, 49489, 99872, 194245, 364432, 660821, 1160932, 1981045, 3291704, 5338066, 8466235, 13156911, 20067894, 30087214, 44398911, 64563765, 92617576, 131189919, 183646650, 254259817, 348409036, 472818827

Offset: 1

Author

R. H. Hardin, Jan 16 2011

Keywords

• nonn

Comments

Column 8 of A184548.

Examples

			Some solutions for 4 X 10:
..0..0..0..0..0..1..1..1..1..1....0..0..0..0..0..0..0..0..0..1
..0..0..1..1..1..1..1..1..1..1....0..0..0..0..0..0..0..0..0..1
..0..0..1..1..1..1..1..1..1..1....0..0..0..0..0..0..0..0..1..0
..1..1..1..1..1..1..1..1..1..1....0..0..0..0..0..1..1..1..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A184548.

Formula

Empirical: a(n) = (1/3628800)*n^10 + (1/48384)*n^9 + (83/120960)*n^8 + (107/8064)*n^7 + (28573/172800)*n^6 + (5323/3840)*n^5 + (1434973/181440)*n^4 + (366371/12096)*n^3 + (2399357/12600)*n^2 + (151541/420)*n + 91.

Conjectures from Colin Barker, Apr 14 2018: (Start)

G.f.: x*(682 - 5502*x + 20347*x^2 - 44828*x^3 + 64744*x^4 - 63833*x^5 + 43442*x^6 - 20156*x^7 + 6118*x^8 - 1104*x^9 + 91*x^10) / (1 - x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.

(End)