A207452 Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

42, 1764, 10710, 36456, 92610, 196812, 370734, 640080, 1034586, 1588020, 2338182, 3326904, 4600050, 6207516, 8203230, 10645152, 13595274, 17119620, 21288246, 26175240, 31858722, 38420844, 45947790, 54529776, 64261050, 75239892, 87568614

Offset

1,1

Comments

Column 7 of A207453.

Links

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

Formula

Empirical: a(n) = 168*n^4 - 84*n^3 - 84*n^2 + 42*n.

Conjectures from Colin Barker, Jun 23 2018: (Start)

G.f.: 42*x*(1 + 37*x + 55*x^2 + 3*x^3) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

Some solutions for n=5:
  0 1 1 0 1 1 1      0 1 1 1 1 1 1      0 1 0 1 0 1 1
  1 1 0 1 1 1 1      1 1 0 1 0 1 0      0 1 0 1 1 1 1
  0 1 0 1 0 1 1      1 1 0 1 0 1 0      0 1 0 1 0 1 1
  0 1 0 1 0 1 0      0 1 0 1 0 1 0      0 1 0 1 0 1 0
  0 1 0 1 0 1 0      0 1 0 1 0 1 0      0 1 0 1 0 1 0

Crossrefs

Cf. A207453.

Sequence in context: A207773 A207900 A207660 * A208554 A207922 A208702

Adjacent sequences: A207449 A207450 A207451 * A207453 A207454 A207455

Keyword

nonn

Author

R. H. Hardin, Feb 17 2012

Status

approved