A164755 Number of nX3 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 2 neighbors with the same value

8, 80, 258, 480, 644, 752, 850, 956, 1070, 1184, 1298, 1412, 1526, 1640, 1754, 1868, 1982, 2096, 2210, 2324, 2438, 2552, 2666, 2780, 2894, 3008, 3122, 3236, 3350, 3464, 3578, 3692, 3806, 3920, 4034, 4148, 4262

Offset

2,1

Links

Table of n, a(n) for n=2..38.

Formula

Empirical: a(n)=2*a(n-1)-a(n-2) for n>=11

Example

Some solutions for n=4
...1.1.2...1.1.2...1.2.2...1.2.2...1.1.2...1.2.2...1.2.2...1.2.2...1.4.2
...1.1.2...3.2.2...1.2.4...1.3.4...1.2.2...2.2.3...1.2.2...1.1.4...1.4.2
...3.4.2...3.2.4...2.2.4...1.3.4...3.3.4...3.3.3...1.4.4...3.1.4...1.4.2
...3.4.4...3.4.4...3.4.4...3.3.4...3.3.4...3.4.4...3.3.4...3.4.4...3.4.4
------
...1.2.2...1.1.2...1.2.2...1.2.2...1.1.2...1.1.2...1.1.2...1.2.2...1.1.2
...3.3.2...3.1.2...1.1.2...1.1.2...1.4.2...1.2.2...3.1.2...1.1.2...2.2.2
...3.4.2...3.2.2...3.1.2...3.1.2...1.4.2...1.2.4...3.2.2...3.1.4...2.4.4
...3.4.4...3.3.4...3.3.4...3.1.4...3.4.4...3.4.4...3.4.4...3.1.4...3.3.4

Crossrefs

Sequence in context: A069543 A144410 A188149 * A050799 A100431 A173116

Adjacent sequences: A164752 A164753 A164754 * A164756 A164757 A164758

Keyword

nonn

Author

R. H. Hardin Aug 24 2009

Status

approved