A184545 Number of (n+2) X 8 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

415, 1114, 2413, 4774, 8989, 16345, 28844, 49489, 82648, 134509, 213640, 331669, 504100, 751282, 1099549, 1582550, 2242789, 3133396, 4320151, 5883784, 7922575, 10555279, 13924402, 18199855, 23583014, 30311215, 38662714, 48962143, 61586494

Offset

1,1

Comments

Column 6 of A184548.

Links

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

Formula

Empirical: a(n) = (1/40320)*n^8 + (13/10080)*n^7 + (83/2880)*n^6 + (13/36)*n^5 + (15967/5760)*n^4 + (19201/1440)*n^3 + (121183/1120)*n^2 + (12673/56)*n + 64.

Conjectures from Colin Barker, Apr 13 2018: (Start)

G.f.: x*(415 - 2621*x + 7327*x^2 - 11699*x^3 + 11605*x^4 - 7310*x^5 + 2861*x^6 - 641*x^7 + 64*x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

Example

Some solutions for 4 X 8:
  0 0 0 0 0 0 0 0     0 0 0 0 0 0 0 0     0 0 0 0 0 0 0 0
  0 0 0 0 0 0 1 1     0 0 0 0 0 0 0 0     0 0 0 0 0 0 1 1
  0 0 0 0 0 1 0 1     0 0 0 0 0 0 1 1     0 0 0 0 0 1 0 0
  0 0 0 1 1 1 1 1     0 0 0 1 1 1 0 0     0 0 0 0 0 1 1 1

Crossrefs

Cf. A184548.

Sequence in context: A332141 A187864 A190028 * A096032 A166057 A306381

Adjacent sequences: A184542 A184543 A184544 * A184546 A184547 A184548

Keyword

nonn

Author

R. H. Hardin, Jan 16 2011

Status

approved