A202195 Number of (n+2) X 3 binary arrays avoiding patterns 001 and 101 in rows and columns.

108, 240, 450, 756, 1176, 1728, 2430, 3300, 4356, 5616, 7098, 8820, 10800, 13056, 15606, 18468, 21660, 25200, 29106, 33396, 38088, 43200, 48750, 54756, 61236, 68208, 75690, 83700, 92256, 101376, 111078, 121380, 132300, 143856, 156066, 168948

Offset

1,1

Comments

Column 1 of A202202.

Links

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

Formula

Empirical: a(n) = 3*(n+3)*(n+2)^2 = 3*A011379(n+2).

Conjectures from Colin Barker, Mar 03 2018: (Start)

G.f.: 6*x*(18 - 32*x + 23*x^2 - 6*x^3) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)

Example

Some solutions for n=10:
  0 0 0    0 0 0    1 0 0    1 0 0    1 0 0    0 1 1    0 1 1
  1 1 1    0 1 1    0 1 1    1 1 0    1 1 1    1 1 1    1 1 1
  1 1 0    0 1 1    0 1 1    0 1 0    1 1 1    1 1 1    1 1 1
  1 1 0    0 1 1    0 1 1    0 1 0    1 1 0    1 1 1    1 1 1
  1 1 0    0 1 1    0 1 0    0 1 0    1 0 0    1 1 1    1 1 1
  0 1 0    0 1 1    0 0 0    0 1 0    0 0 0    1 1 1    1 1 0
  0 1 0    0 1 1    0 0 0    0 1 0    0 0 0    1 1 0    1 0 0
  0 1 0    0 1 1    0 0 0    0 0 0    0 0 0    1 1 0    0 0 0
  0 1 0    0 1 0    0 0 0    0 0 0    0 0 0    0 1 0    0 0 0
  0 1 0    0 1 0    0 0 0    0 0 0    0 0 0    0 1 0    0 0 0
  0 1 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 0    0 0 0    0 0 0    0 0 0

Crossrefs

Cf. A202202.

Sequence in context: A275996 A235292 A202202 * A242867 A255091 A255084

Adjacent sequences: A202192 A202193 A202194 * A202196 A202197 A202198

Keyword

nonn

Author

R. H. Hardin, Dec 14 2011

Status

approved