A210055 Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having one, two or four distinct values, and new values 0..3 introduced in row major order.

51, 646, 8767, 124097, 1800963, 26510247, 393310267, 5860240451, 87518315915, 1308643997211, 19580912760811, 293088590922763, 4387807244096555, 65696214148675179, 983686592529709995, 14729424345053396011

Offset

1,1

Comments

Column 2 of A210061.

Links

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

Formula

Empirical: a(n) = 29*a(n-1) - 266*a(n-2) + 902*a(n-3) - 968*a(n-4) + 176*a(n-5) + 128*a(n-6).

Empirical g.f.: x*(51 - 833*x + 3599*x^2 - 4312*x^3 + 848*x^4 + 640*x^5) / ((1 - x)*(1 - 8*x)*(1 - 20*x + 78*x^2 - 40*x^3 - 16*x^4)). - Colin Barker, Jul 14 2018

Example

Some solutions for n=4:
..0..1..0....0..1..1....0..0..0....0..0..0....0..0..1....0..1..0....0..0..0
..0..1..0....2..3..3....0..0..0....1..0..1....0..1..0....1..0..0....0..1..0
..0..1..0....3..2..2....0..1..1....1..0..0....2..3..2....1..0..2....2..3..2
..0..1..1....2..2..0....0..1..1....0..0..0....0..1..0....3..2..2....1..0..1
..0..0..0....1..1..3....2..3..1....0..1..0....0..1..0....1..0..0....0..1..0

Crossrefs

Cf. A210061.

Sequence in context: A166820 A269438 A269622 * A020278 A160829 A160835

Adjacent sequences: A210052 A210053 A210054 * A210056 A210057 A210058

Keyword

nonn

Author

R. H. Hardin, Mar 16 2012

Status

approved