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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A123605 A273743 A089613 * A204467 A062728 A273982

Adjacent sequences:  A164751 A164752 A164753 * A164755 A164756 A164757

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 24 2009

STATUS

approved

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Last modified February 24 18:29 EST 2021. Contains 341577 sequences. (Running on oeis4.)