A202051 Number of (n+2) X 9 binary arrays avoiding patterns 001 and 110 in rows and columns.

1926, 7848, 25650, 71964, 180054, 411696, 874998, 1750140, 3325410, 6046344, 10581246, 17906868, 29418570, 47069856, 73546794, 112483476, 168725358, 248648040, 360539802, 515057004, 725762286, 1009756368, 1388415150

Offset

1,1

Comments

Column 7 of A202052.

Links

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

Formula

Empirical: a(n) = (1/10080)*n^9 + (3/560)*n^8 + (211/1680)*n^7 + (67/40)*n^6 + (6709/480)*n^5 + (6041/80)*n^4 + (663941/2520)*n^3 + (79913/140)*n^2 + (4735/7)*n + 324.

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

G.f.: 18*x*(107 - 634*x + 1880*x^2 - 3472*x^3 + 4298*x^4 - 3652*x^5 + 2114*x^6 - 800*x^7 + 179*x^8 - 18*x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

Example

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

Crossrefs

Cf. A202052.

Sequence in context: A363821 A255867 A326018 * A283949 A133301 A258841

Adjacent sequences: A202048 A202049 A202050 * A202052 A202053 A202054

Keyword

nonn

Author

R. H. Hardin, Dec 10 2011

Status

approved