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A271034 T(n,k)=Number of nXnXn triangular 0..k arrays with some element less than a w, nw or ne neighbor exactly once.

%I A271034 #4 Mar 29 2016 07:46:21
%S A271034 0,0,2,0,8,10,0,20,72,34,0,40,294,450,98,0,70,896,3114,2420,258,0,112,
%T A271034 2268,15116,29120,12010,642,0,168,5040,58036,232432,256020,56754,1538,
%U A271034 0,240,10164,188034,1402082,3441072,2173554,259628,3586,0,330,19008,535106
%N A271034 T(n,k)=Number of nXnXn triangular 0..k arrays with some element less than a w, nw or ne neighbor exactly once.
%C A271034 Table starts
%C A271034 ....0.......0.........0...........0............0..............0...............0
%C A271034 ....2.......8........20..........40...........70............112.............168
%C A271034 ...10......72.......294.........896.........2268...........5040...........10164
%C A271034 ...34.....450......3114.......15116........58036.........188034..........535106
%C A271034 ...98....2420.....29120......232432......1402082........6872424........28658242
%C A271034 ..258...12010....256020.....3441072.....33505396......255757328......1610555756
%C A271034 ..642...56754...2173554....50108414....804566180.....9790184488.....95420380090
%C A271034 .1538..259628..18060096...724727082..19525545192...386105784866...5945425725202
%C A271034 .3586.1160936.147976270.10461499634.479803630966.15669594394610.387907415514308
%H A271034 R. H. Hardin, <a href="/A271034/b271034.txt">Table of n, a(n) for n = 1..146</a>
%F A271034 Empirical for column k:
%F A271034 k=1: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3)
%F A271034 Empirical for row n:
%F A271034 n=2: a(n) = (1/3)*n^3 + n^2 + (2/3)*n
%F A271034 n=3: [polynomial of degree 6]
%F A271034 n=4: [polynomial of degree 10]
%F A271034 n=5: [polynomial of degree 15]
%F A271034 n=6: [polynomial of degree 21]
%e A271034 Some solutions for n=4 k=4
%e A271034 .....0........0........0........1........0........1........0........0
%e A271034 ....0.0......0.3......1.0......2.3......0.0......1.1......0.2......0.0
%e A271034 ...1.0.0....3.3.3....3.4.4....3.4.4....0.1.3....0.1.2....0.2.2....1.1.0
%e A271034 ..1.1.1.1..4.4.3.4..4.4.4.4..3.3.4.4..2.4.3.3..2.3.4.4..0.0.2.3..4.4.4.4
%Y A271034 Column 1 is A036799(n-1).
%Y A271034 Row 2 is A007290(n+2).
%K A271034 nonn,tabl
%O A271034 1,3
%A A271034 _R. H. Hardin_, Mar 29 2016