A241345 Number of n X 2 0..3 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..3 introduced in row major order.

1, 2, 5, 22, 103, 519, 2656, 13798, 72005, 377132, 1978263, 10387415, 54569162, 286758658, 1507147669, 7922014506, 41642626111, 218903934463, 1150737770732, 6049275496670, 31800411817677, 167171979847160, 878810026664375

Offset

1,2

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 8*a(n-2) - 48*a(n-3) + 59*a(n-4) + 102*a(n-5) - 77*a(n-6) - 112*a(n-7) + 38*a(n-8) + 66*a(n-9) - 27*a(n-10) for n>11.

Empirical g.f.: x*(1 - 6*x - 3*x^2 + 46*x^3 + 4*x^4 - 109*x^5 - 38*x^6 + 104*x^7 + 31*x^8 - 51*x^9 + 9*x^10) / ((1 - x)*(1 - 3*x)*(1 - x - 2*x^2 - x^3 + x^4)*(1 - 3*x - 12*x^2 - x^3 + 9*x^4)). - Colin Barker, Oct 30 2018

Example

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

Crossrefs

Column 2 of A241349.

Sequence in context: A369830 A056840 A321608 * A272821 A278439 A126797

Adjacent sequences: A241342 A241343 A241344 * A241346 A241347 A241348

Keyword

nonn

Author

R. H. Hardin, Apr 19 2014

Status

approved