A197403 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

3, 9, 20, 71, 227, 664, 2107, 6675, 20696, 65029, 205057, 643930, 2026105, 6384135, 20104382, 63329883, 199576691, 628932096, 1982100085, 6247388117, 19691746204, 62069757373, 195654894641, 616749232724, 1944155102539, 6128552692107

Offset

1,1

Comments

Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's.

Column 2 of A197409.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 4*a(n-2) + 7*a(n-3) - 10*a(n-4) - 39*a(n-5) - 30*a(n-6) - 12*a(n-7) + 5*a(n-8) + 2*a(n-9).

Empirical g.f.: x*(1 + x)^2*(3 - 3*x - 7*x^2 - 9*x^3 - 3*x^4 + 8*x^5 + 2*x^6) / (1 - 2*x - 4*x^2 - 7*x^3 + 10*x^4 + 39*x^5 + 30*x^6 + 12*x^7 - 5*x^8 - 2*x^9). - Colin Barker, Mar 01 2018

Example

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

Crossrefs

Cf. A197409.

Sequence in context: A196294 A196212 A146219 * A305618 A006077 A291898

Adjacent sequences: A197400 A197401 A197402 * A197404 A197405 A197406

Keyword

nonn

Author

R. H. Hardin, Oct 14 2011

Status

approved