A188097 Number of (n+3) X 4 binary arrays with every 4 X 4 subblock commuting with each horizontal and vertical neighbor 4 X 4 subblock.

65536, 708, 1417, 3594, 8274, 13814, 17850, 20888, 24117, 26596, 29585, 35384, 46623, 63199, 84577, 111803, 147698, 191409, 242911, 306060, 389117, 496566, 633184, 808675, 1039969, 1339366, 1719434, 2201524, 2822474, 3618976, 4632767

Offset

1,1

Comments

Column 1 of A188105.

Links

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

Formula

Empirical: a(n) = 2*a(n-1)-a(n-2)+a(n-4)-2*a(n-5)+a(n-6)+a(n-8)-a(n-9) for n>15.

Empirical g.f.: x*(65536 - 130364*x + 65537*x^2 + 1468*x^3 - 63033*x^4 + 131224*x^5 - 67041*x^6 - 2466*x^7 - 67848*x^8 + 63218*x^9 + 1305*x^10 + 1631*x^11 + 569*x^12 + 547*x^13 + 256*x^14) / ((1 - x)*(1 - x - x^4 + x^5 - x^8)). - Colin Barker, Feb 07 2018

Example

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

Crossrefs

Sequence in context: A069391 A188096 A188105 * A223602 A223695 A202939

Adjacent sequences: A188094 A188095 A188096 * A188098 A188099 A188100

Keyword

nonn

Author

R. H. Hardin, Mar 20 2011

Status

approved