A164754 Number of n X 2 1..4 arrays with all 1's connected, all 2's connected, all 3's connected, all 4's 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.

1, 8, 25, 50, 83, 124, 173, 230, 295, 368, 449, 538, 635, 740, 853, 974, 1103, 1240, 1385, 1538, 1699, 1868, 2045, 2230, 2423, 2624, 2833, 3050, 3275, 3508, 3749, 3998, 4255, 4520, 4793, 5074, 5363, 5660, 5965, 6278, 6599, 6928, 7265, 7610, 7963, 8324, 8693

Offset: 2

Author

R. H. Hardin, Aug 24 2009

Keywords

• nonn

Examples

			Some solutions for n=9:
...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2
...1.4...1.3...1.4...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2
...1.4...3.3...1.4...1.2...1.2...1.1...2.2...1.2...3.2...1.1...1.2...1.2...1.2
...1.4...3.4...1.4...1.2...1.2...4.1...2.3...1.2...3.2...3.1...1.2...1.1...1.4
...1.4...3.4...1.4...1.2...1.2...4.1...2.3...2.2...3.2...3.1...3.2...4.4...1.4
...1.4...3.4...3.4...2.2...1.1...4.1...2.3...2.3...3.2...3.1...3.2...3.4...3.4
...1.4...3.4...3.4...2.3...4.4...4.4...3.3...2.3...3.4...3.1...3.2...3.4...3.4
...3.4...3.4...3.4...3.3...3.4...3.4...3.4...3.3...3.4...3.1...3.4...3.4...3.4
...3.4...3.4...3.4...3.4...3.4...3.4...3.4...3.4...3.4...3.4...3.4...3.4...3.4
		

Links

• R. H. Hardin, Table of n, a(n) for n=2..100

Programs

Mathematica

Join[{1}, Table[n*(4*n - 3) - 2, {n, 2, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>=6.

Empirical g.f.: x^2*(1 + 5*x + 4*x^2 - 2*x^3) / (1 - x)^3. - Colin Barker, Mar 25 2018

Empirical: a(n) = 4*(n-2)^2 + 5*(n-2) -1 for n>=3. - Bill McEachen, Aug 31 2020