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, 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

R. H. Hardin, Table of n, a(n) for n = 1..37

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: A125128 A034334 A036891 * A340567 A268775 A294840

Adjacent sequences: A183273 A183274 A183275 * A183277 A183278 A183279

Keyword

nonn

Author

R. H. Hardin, Jan 03 2011

Status

approved