A206629 - OEIS

A206629

Number of (n+1) X 3 0..2 arrays with every 2 X 3 or 3 X 2 subblock having no more than four equal edges, and new values 0..2 introduced in row major order.

%I #9 Jun 17 2018 08:09:01

%S 121,3232,86392,2309200,61723264,1649819344,44098506880,1178721971776,

%T 31506406571584,842144015978368,22509915310006528,601674152698239232,

%U 16082325545854547968,429869213764553543680,11490100757858808902656

%N Number of (n+1) X 3 0..2 arrays with every 2 X 3 or 3 X 2 subblock having no more than four equal edges, and new values 0..2 introduced in row major order.

%C Column 2 of A206635.

%H R. H. Hardin, <a href="/A206629/b206629.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 24*a(n-1) + 68*a(n-2) + 132*a(n-3) + 8*a(n-4) + 48*a(n-5).

%F Empirical g.f.: x*(121 + 328*x + 596*x^2 + 44*x^3 + 216*x^4) / (1 - 24*x - 68*x^2 - 132*x^3 - 8*x^4 - 48*x^5). - _Colin Barker_, Jun 17 2018

%e Some solutions for n=4:

%e ..0..0..0....0..0..1....0..0..0....0..0..0....0..0..1....0..0..1....0..1..0

%e ..0..1..1....0..0..0....0..1..0....0..1..0....2..0..2....1..1..1....2..1..2

%e ..1..0..1....2..2..1....2..0..1....0..0..2....1..0..2....1..0..1....2..1..1

%e ..2..2..1....2..0..0....2..0..1....1..0..0....1..2..1....2..1..2....0..1..1

%e ..0..1..1....2..0..0....0..0..2....2..0..0....2..2..1....0..1..2....0..0..2

%Y Cf. A206635.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 10 2012