%I #4 Mar 20 2016 11:00:51
%S 0,0,6,0,0,0,0,36,0,0,0,36,312,0,0,0,96,1716,8808,0,0,0,120,8148,
%T 171576,443088,0,0,0,204,23448,1728288,46957788,44168712,0,0,0,252,
%U 67788,13177740,1008327378,38923001616,8708857332,0,0,0,360,144252,70129212
%N T(n,k)=Number of nXnXn triangular 0..k arrays with some element plus some adjacent element totalling k+1 or k-1 exactly once.
%C Table starts
%C .0.0........0...........0.............0...............0................0
%C .6.0.......36..........36............96.............120..............204
%C .0.0......312........1716..........8148...........23448............67788
%C .0.0.....8808......171576.......1728288........13177740.........70129212
%C .0.0...443088....46957788....1008327378.....25162747992.....271906503420
%C .0.0.44168712.38923001616.1749723617976.176610474548304.4288332432901128
%H R. H. Hardin, <a href="/A270606/b270606.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for row n:
%F n=2: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>5
%F n=3: [order 10] for n>17
%F n=4: [order 18] for n>33
%F Empirical quasipolynomials for row n:
%F n=2: polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2 for n>1
%F n=3: polynomial of degree 5 plus a quasipolynomial of degree 3 with period 2 for n>7
%F n=4: polynomial of degree 9 plus a quasipolynomial of degree 7 with period 2 for n>15
%e Some solutions for n=4 k=4
%e .....0........0........4........0........0........0........2........3
%e ....0.4......0.1......0.4......0.0......0.0......0.1......0.1......1.1
%e ...0.4.4....3.1.3....1.3.3....4.4.2....0.0.0....0.0.3....0.0.0....1.3.1
%e ..0.0.0.3..1.3.3.4..3.1.1.3..2.0.4.3..0.1.4.2..4.0.1.3..0.4.4.0..0.0.1.3
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Mar 20 2016