%I #4 Mar 29 2016 07:49:40

%S 258,12010,256020,3441072,33505396,255757328,1610555756,8669119882,

%T 40937078274,172973004078,664139482668,2345904959628,7699860067962,

%U 23679297338148,68702482342180,189162014324890,496732138963680

%N Number of 6X6X6 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.

%C Row 6 of A271034.

%H R. H. Hardin, <a href="/A271038/b271038.txt">Table of n, a(n) for n = 1..26</a>

%F Empirical: a(n) = (3307/154821036883968000)*n^21 + (277057/110586454917120000)*n^20 + (1603411/11585247657984000)*n^19 + (2270033/474249904128000)*n^18 + (30996697/266765571072000)*n^17 + (101572363/48283361280000)*n^16 + (77666311187/2636271525888000)*n^15 + (123014962363/376610217984000)*n^14 + (11598452441/3985293312000)*n^13 + (2030854507051/96566722560000)*n^12 + (2391727070743/19313344512000)*n^11 + (1044262844011/1755758592000)*n^10 + (1225063692125929/527254305177600)*n^9 + (35232199804051/4803701760000)*n^8 + (1481084911939/80061696000)*n^7 + (575071748810329/15692092416000)*n^6 + (2470455323050879/44460928512000)*n^5 + (9812842428469/158336640000)*n^4 + (1957326271199891/41064607584000)*n^3 + (2192821336711/97772875200)*n^2 + (37411763/7759752)*n

%e Some solutions for n=2

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

%e ......0.0..........0.0..........0.0..........0.1..........0.0..........0.2

%e .....0.0.0........0.0.1........0.0.0........0.1.1........0.0.0........0.2.2

%e ....0.0.0.1......1.0.1.1......0.0.0.0......0.1.1.1......0.0.0.1......0.0.2.2

%e ...1.1.0.1.1....1.1.2.2.2....1.1.1.1.1....0.2.2.2.1....0.0.1.1.2....1.2.2.2.2

%e ..1.1.1.2.2.2..1.1.2.2.2.2..2.2.1.1.2.2..1.2.2.2.2.2..1.1.1.1.1.2..1.2.2.2.2.2

%Y Cf. A271034.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 29 2016