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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.
12
0, 0, 2, 0, 8, 10, 0, 20, 72, 34, 0, 40, 294, 450, 98, 0, 70, 896, 3114, 2420, 258, 0, 112, 2268, 15116, 29120, 12010, 642, 0, 168, 5040, 58036, 232432, 256020, 56754, 1538, 0, 240, 10164, 188034, 1402082, 3441072, 2173554, 259628, 3586, 0, 330, 19008, 535106
OFFSET
1,3
COMMENTS
Table starts
....0.......0.........0...........0............0..............0...............0
....2.......8........20..........40...........70............112.............168
...10......72.......294.........896.........2268...........5040...........10164
...34.....450......3114.......15116........58036.........188034..........535106
...98....2420.....29120......232432......1402082........6872424........28658242
..258...12010....256020.....3441072.....33505396......255757328......1610555756
..642...56754...2173554....50108414....804566180.....9790184488.....95420380090
.1538..259628..18060096...724727082..19525545192...386105784866...5945425725202
.3586.1160936.147976270.10461499634.479803630966.15669594394610.387907415514308
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3)
Empirical for row n:
n=2: a(n) = (1/3)*n^3 + n^2 + (2/3)*n
n=3: [polynomial of degree 6]
n=4: [polynomial of degree 10]
n=5: [polynomial of degree 15]
n=6: [polynomial of degree 21]
EXAMPLE
Some solutions for n=4 k=4
.....0........0........0........1........0........1........0........0
....0.0......0.3......1.0......2.3......0.0......1.1......0.2......0.0
...1.0.0....3.3.3....3.4.4....3.4.4....0.1.3....0.1.2....0.2.2....1.1.0
..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
CROSSREFS
Column 1 is A036799(n-1).
Row 2 is A007290(n+2).
Sequence in context: A181592 A332616 A097348 * A185965 A106193 A334875
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 29 2016
STATUS
approved