A185489 Number of (n+1) X 2 binary arrays with every 2 X 2 subblock sum equal to some horizontal or vertical neighbor 2 X 2 subblock sum.

0, 24, 36, 160, 380, 1332, 3616, 11828, 33764, 107240, 314028, 980996, 2915008, 9013892, 27021076, 83023720, 250222428, 765753844, 2315518240, 7068457300, 21417487492, 65277991272, 198042102732, 603022088996, 1830890468736

Offset

1,2

Comments

Column 1 of A185497.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 3*a(n-2) - 14*a(n-3) + 24*a(n-4) - 16*a(n-5) - 24*a(n-6) + 16*a(n-7) - 64*a(n-8).

Empirical g.f.: 4*x^2*(6 - 9*x - 5*x^2 + 32*x^3 - 90*x^4 + 60*x^5 - 96*x^6) / ((1 - 2*x)*(1 - x - 5*x^2 + 4*x^3 - 16*x^4 - 16*x^5 - 8*x^6 - 32*x^7)). - Colin Barker, Feb 27 2018

Example

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

Crossrefs

Cf. A185497.

Sequence in context: A327946 A288949 A108190 * A303884 A304616 A172424

Adjacent sequences: A185486 A185487 A185488 * A185490 A185491 A185492

Keyword

nonn

Author

R. H. Hardin, Jan 29 2011

Status

approved