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.

8, 104, 670, 3096, 11786, 39564, 121678, 350992, 964338, 2550356, 6541846, 16366616, 40107066, 96586332, 229176926, 536895520, 1243957122, 2854431844, 6494293670, 14664265256, 32889555658, 73320539244, 162562734830

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: A190786 A138430 A366653 * A335608 A109774 A001657

Adjacent sequences: A164757 A164758 A164759 * A164761 A164762 A164763

Keyword

nonn

Author

R. H. Hardin, Aug 24 2009

Status

approved