A207436 Number of n X 2 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.

4, 16, 36, 81, 196, 484, 1225, 3136, 8100, 21025, 54756, 142884, 373321, 976144, 2553604, 6682225, 17489124, 45778756, 119836809, 313714944, 821280964, 2150084161, 5628900676, 14736503236, 38580423561, 101004467344, 264432492900

Offset

1,1

Comments

Column 2 of A207442.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 6*a(n-3) + 4*a(n-4) + 2*a(n-5) - a(n-6) for n > 7.

Empirical g.f.: x*(4 - 20*x^2 - 7*x^3 + 24*x^4 + 6*x^5 - 5*x^6) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)). - Colin Barker, Feb 17 2018

Empirical: a(n) = 1 - 2*A033999(n)/5 +2*A000045(n+2) +7*A001906(n+1)/5 -3*A001906(n)/5 for n>1. - R. J. Mathar, Nov 09 2018

Example

Some solutions for n=4:
  1 0   0 1   0 1   1 1   0 0   0 0   1 0   1 1   1 1   0 1
  0 1   1 0   1 1   1 1   1 0   0 1   1 1   1 1   0 0   1 0
  1 1   0 1   1 0   1 1   1 0   0 0   1 1   1 1   1 1   1 1
  1 0   1 1   1 1   1 1   0 0   0 1   1 1   0 0   0 0   1 0

Crossrefs

Sequence in context: A207025 A207170 A207069 * A189145 A005722 A075408

Adjacent sequences: A207433 A207434 A207435 * A207437 A207438 A207439

Keyword

nonn

Author

R. H. Hardin, Feb 17 2012

Status

approved