A202050 Number of (n+2) X 8 binary arrays avoiding patterns 001 and 110 in rows and columns.

1392, 5216, 15760, 41088, 95984, 205792, 411696, 777760, 1400080, 2418432, 4030832, 6511456, 10232400, 15689792, 23534800, 34610112, 49992496, 71042080, 99459024, 137348288, 187293232, 252438816, 336585200, 444292576, 580998096

Offset: 1

Author

R. H. Hardin, Dec 10 2011

Keywords

• nonn

Comments

Column 6 of A202052.

Examples

			Some solutions for n=3:
  0 0 0 0 0 0 0 0     0 1 0 1 0 1 0 1     1 0 1 1 1 1 1 1
  0 1 0 1 0 0 0 0     1 0 1 0 1 0 0 0     0 1 0 0 0 0 0 0
  0 1 0 0 0 0 0 0     0 1 0 1 0 1 0 1     1 0 1 1 1 1 1 1
  0 1 0 1 0 0 0 0     0 1 0 1 0 0 0 0     0 1 0 0 0 0 0 0
  0 1 0 1 0 0 0 0     0 1 0 1 0 1 0 1     1 0 1 0 1 0 0 0
		

Links

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

Crossrefs

Cf. A202052.

Formula

Empirical: a(n) = (1/1260)*n^8 + (11/315)*n^7 + (59/90)*n^6 + (308/45)*n^5 + (7807/180)*n^4 + (7667/45)*n^3 + (14139/35)*n^2 + (17876/35)*n + 256.

Conjectures from Colin Barker, May 26 2018: (Start)

G.f.: 16*x*(87 - 457*x + 1183*x^2 - 1869*x^3 + 1925*x^4 - 1307*x^5 + 567*x^6 - 143*x^7 + 16*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)