A183276 - OEIS

%I #8 Mar 27 2018 08:49:08

%S 1,4,11,26,60,132,290,620,1322,2777,5848,12169,25419,52590,109375,

%T 225532,467758,962536,1993088,4096214,8473290,17401047,35973146,

%U 73841057,152593325,313133216,646942003,1327337686,2741920392,5625006348

%N Half the number of n X n X n triangular binary arrays with each element having no more than two neighbors unequal to itself.

%H R. H. Hardin, <a href="/A183276/b183276.txt">Table of n, a(n) for n = 1..37</a>

%F 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).

%F 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

%e Some solutions for 5 X 5 X 5 with a(1,1)=0:

%e ......0..........0..........0..........0..........0..........0..........0

%e .....1.1........0.0........0.1........1.1........0.0........1.1........0.0

%e ....1.1.1......0.0.0......0.1.1......1.1.1......0.0.1......1.1.1......0.0.0

%e ...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

%e ..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

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 03 2011