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A164760 Number of n X 3 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 3 neighbors with the same value. 1
8, 104, 670, 3096, 11786, 39564, 121678, 350992, 964338, 2550356, 6541846, 16366616, 40107066, 96586332, 229176926, 536895520, 1243957122, 2854431844, 6494293670, 14664265256, 32889555658, 73320539244, 162562734830 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

R. H. Hardin, Table of n, a(n) for n=2..50

FORMULA

Empirical: a(n) = 10*a(n-1) - 42*a(n-2) + 96*a(n-3) - 129*a(n-4) + 102*a(n-5) - 44*a(n-6) + 8*a(n-7) for n>=9.

Conjectures from Colin Barker, Mar 25 2018: (Start)

G.f.: 2*x^2*(4 + 12*x - 17*x^2 - 2*x^3 + 7*x^4 + 8*x^5 + 4*x^6) / ((1 - x)^4*(1 - 2*x)^3).

a(n) = (-4236 + 4281*2^n - 4*(421+339*2^n)*n + 6*(-32+25*2^n)*n^2 - 32*n^3) / 6.

(End)

EXAMPLE

Some solutions for n=4:

...1.1.2...1.2.2...1.1.2...1.2.2...1.1.2...1.2.2...1.1.2...1.3.2...1.1.2

...2.2.2...4.2.2...3.1.2...1.1.2...1.2.2...3.2.4...1.1.2...1.3.2...1.3.2

...2.2.2...4.4.4...3.3.4...3.4.4...3.3.4...3.2.4...2.2.2...1.3.3...3.3.2

...3.4.4...3.3.4...3.4.4...3.3.4...3.4.4...3.2.4...3.3.4...3.3.4...3.3.4

------

...1.1.2...1.2.2...1.1.2...1.1.2...1.4.2...1.1.2...1.1.2...1.1.2...1.1.2

...2.2.2...3.2.4...1.1.2...1.4.2...3.4.2...2.2.2...1.1.2...4.4.2...2.2.2

...3.2.4...3.2.4...4.4.2...1.4.2...3.4.4...3.4.2...1.1.2...3.4.4...3.3.2

...3.2.4...3.3.4...3.4.4...3.4.4...3.4.4...3.4.4...3.4.4...3.4.4...3.3.4

CROSSREFS

Sequence in context: A222664 A190786 A138430 * A335608 A109774 A001657

Adjacent sequences:  A164757 A164758 A164759 * A164761 A164762 A164763

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 24 2009

STATUS

approved

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Last modified January 16 04:59 EST 2022. Contains 350374 sequences. (Running on oeis4.)