A204637 Number of (n+2) X 5 0..3 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..3 introduced in row major order.

1781, 5974, 248, 933, 760, 2517, 9750, 28856, 108520, 412247, 1538786, 5831457, 22111228, 83757474, 317540856, 1203895697, 4564096372, 17303777693, 65603619578, 248721544020, 942974882152, 3575089249203, 13554190415694

Offset

1,1

Comments

Column 3 of A204642.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) -3*a(n-2) -4*a(n-3) -12*a(n-4) +12*a(n-5) +21*a(n-6) -9*a(n-7) -9*a(n-8) for n>10.

Empirical g.f.: x*(1781 - 2931*x - 24279*x^2 + 24739*x^3 + 42107*x^4 + 52824*x^5 - 102936*x^6 - 110508*x^7 + 66069*x^8 + 52704*x^9) / ((1 - x)*(1 - x - x^2)*(1 - 3*x - 3*x^2)*(1 - 3*x^3)). - Colin Barker, Jun 08 2018

Example

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

Crossrefs

Cf. A204642.

Sequence in context: A237906 A187524 A253057 * A023088 A251086 A255157

Adjacent sequences: A204634 A204635 A204636 * A204638 A204639 A204640

Keyword

nonn

Author

R. H. Hardin, Jan 17 2012

Status

approved