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

Author

R. H. Hardin, Jan 16 2011

Keywords

• nonn

Comments

Column 6 of A184548.

Examples

			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
		

Links

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

Crossrefs

Cf. A184548.

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)