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

1,1

Comments

Column 8 of A184548.

Links

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

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)

Example

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

Crossrefs

Cf. A184548.

Sequence in context: A043577 A043763 A200860 * A327417 A145321 A175155

Adjacent sequences: A184544 A184545 A184546 * A184548 A184549 A184550

Keyword

nonn

Author

R. H. Hardin, Jan 16 2011

Status

approved