A206339 Number of (n+1) X 5 0..3 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.

296, 534, 682, 1581, 2034, 4711, 6078, 14101, 18210, 42271, 54606, 126799, 163806, 380385, 491406, 1141143, 1474206, 3423417, 4422606, 10270239, 13267806, 30810705, 39803406, 92432103, 119410206, 277296297, 358230606, 831888879

Offset

1,1

Comments

Column 4 of A206343.

Links

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

Formula

Empirical: a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) for n>13.

Empirical g.f.: x*(296 + 238*x - 740*x^2 + 185*x^3 + 9*x^4 - 20*x^5 + 8*x^6 - 8*x^7 + 8*x^8 - 8*x^9 + 8*x^10 + 10*x^11 + 2*x^12) / ((1 - x)*(1 - 3*x^2)). - Colin Barker, Jun 15 2018

Example

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

Crossrefs

Cf. A206343.

Sequence in context: A238512 A003780 A338592 * A107924 A224170 A223861

Adjacent sequences: A206336 A206337 A206338 * A206340 A206341 A206342

Keyword

nonn

Author

R. H. Hardin, Feb 06 2012

Status

approved