login
A183276
Half the number of n X n X n triangular binary arrays with each element having no more than two neighbors unequal to itself.
1
1, 4, 11, 26, 60, 132, 290, 620, 1322, 2777, 5848, 12169, 25419, 52590, 109375, 225532, 467758, 962536, 1993088, 4096214, 8473290, 17401047, 35973146, 73841057, 152593325, 313133216, 646942003, 1327337686, 2741920392, 5625006348
OFFSET
1,2
LINKS
FORMULA
Empirical: a(n) = a(n-1) + 4*a(n-2) - 3*a(n-3) + 3*a(n-4) - 6*a(n-5) - 9*a(n-6) + 3*a(n-7) + 2*a(n-8) + a(n-9) + a(n-10).
Empirical g.f.: x*(1 + 3*x + 3*x^2 + 2*x^3 - x^4 - 5*x^5 - 4*x^6 + 3*x^7 - x^8 + x^9) / ((1 - x - x^2)*(1 + x^2 - x^4)*(1 - 4*x^2 - x^4)). - Colin Barker, Mar 27 2018
EXAMPLE
Some solutions for 5 X 5 X 5 with a(1,1)=0:
......0..........0..........0..........0..........0..........0..........0
.....1.1........0.0........0.1........1.1........0.0........1.1........0.0
....1.1.1......0.0.0......0.1.1......1.1.1......0.0.1......1.1.1......0.0.0
...0.0.0.0....1.1.1.1....0.1.1.0....0.0.0.0....0.0.1.1....1.1.1.1....1.1.1.1
..0.0.0.0.0..0.1.1.1.0..0.1.1.0.0..1.0.0.0.1..0.0.1.1.1..0.0.0.0.0..1.1.1.1.0
CROSSREFS
Sequence in context: A034334 A036891 A373358 * A340567 A268775 A294840
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 03 2011
STATUS
approved