A190027 Number of (n+2) X 5 binary arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

228, 79, 158, 274, 362, 430, 506, 610, 790, 1094, 1539, 2128, 2917, 3951, 5309, 7171, 9723, 13188, 17946, 24428, 33181, 45089, 61273, 83193, 113026, 153617, 208697, 283598, 385441, 523693, 711599, 967038, 1313966, 1785449, 2426308, 3296908

Offset

1,1

Comments

Column 3 of A190033.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Robert Israel, Maple-assisted proof of recurrence

Formula

Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5) +a(n-6) -a(n-7) for n>11.

Formula verified: see link. - Robert Israel, Mar 05 2023

Empirical g.f.: x*(228 - 377*x + 228*x^2 - 191*x^3 + 349*x^4 - 248*x^5 - 257*x^6 + 205*x^7 + 17*x^8 + 25*x^10) / ((1 - x)*(1 - x - x^3 + x^4 - x^6)). - Colin Barker, May 03 2018

Example

Some solutions for 4 X 5:
  0 0 0 0 1    0 0 0 0 1    0 0 0 0 0    1 0 0 0 0
  0 0 0 0 1    0 0 0 0 0    0 0 0 0 1    0 0 0 0 1
  1 0 0 0 0    1 0 0 0 0    1 0 0 0 0    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

Crossrefs

Cf. A190033.

Sequence in context: A122976 A098245 A343169 * A090943 A252451 A305063

Adjacent sequences: A190024 A190025 A190026 * A190028 A190029 A190030

Keyword

nonn

Author

R. H. Hardin, May 04 2011

Status

approved