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

2,2

Links

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

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

Example

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

Mathematica

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

Crossrefs

Sequence in context: A273743 A089613 A344714 * A204467 A062728 A273982

Adjacent sequences: A164751 A164752 A164753 * A164755 A164756 A164757

Keyword

nonn

Author

R. H. Hardin, Aug 24 2009

Status

approved