A184607 Half the number of (n+1) X 3 binary arrays with no 2 X 2 subblock sum differing from a horizontal or vertical neighbor subblock sum by more than one.

28, 160, 918, 5430, 32042, 188394, 1107926, 6519094, 38356642, 225665454, 1327676850, 7811308282, 45957316482, 270386512686, 1590799536334, 9359355830962, 55065102381718, 323971594861746, 1906063733817962

Offset

1,1

Comments

Column 2 of A184614.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) + 3*a(n-2) + 10*a(n-3) + 29*a(n-4) - 66*a(n-5) - 20*a(n-6) + 8*a(n-7) - 12*a(n-8) + 8*a(n-9).

Empirical g.f.: 2*x*(14 + 10*x + 17*x^2 + 40*x^3 - 137*x^4 - 39*x^5 + 14*x^6 - 22*x^7 + 16*x^8) / (1 - 5*x - 3*x^2 - 10*x^3 - 29*x^4 + 66*x^5 + 20*x^6 - 8*x^7 + 12*x^8 - 8*x^9). - Colin Barker, Apr 14 2018

Example

Some solutions for 4 X 3:
..1..0..1....1..0..1....0..1..0....1..0..1....0..1..0....0..1..1....0..1..1
..1..0..0....1..0..0....0..1..0....1..0..1....0..1..0....1..0..1....1..1..1
..1..0..1....1..1..1....1..0..0....1..1..1....1..1..0....0..1..0....1..1..1
..0..0..1....1..0..0....1..0..1....0..0..1....0..0..0....0..1..0....1..0..1
...
...2..1.......2..1.......2..2.......2..2.......2..2.......2..3.......3..4...
...2..1.......3..2.......2..1.......3..3.......3..2.......2..2.......4..4...
...1..2.......3..2.......2..1.......2..3.......2..1.......2..2.......3..3...

Crossrefs

Cf. A184614.

Sequence in context: A026910 A172220 A255151 * A215699 A220158 A085377

Adjacent sequences: A184604 A184605 A184606 * A184608 A184609 A184610

Keyword

nonn

Author

R. H. Hardin, Jan 18 2011

Status

approved