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

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

Author

R. H. Hardin, Mar 29 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..146

Crossrefs

Column 1 is A036799(n-1).

Row 2 is A007290(n+2).

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]