editing

approved

R. H. Hardin, <a href="/A271034/b271034.txt">Table of n, a(n) for n = 1..146</a>

allocated for R. H. Hardin

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

1,3

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

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]

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

Column 1 is A036799(n-1).

Row 2 is A007290(n+2).

allocated

nonn,tabl

R. H. Hardin, Mar 29 2016

approved

editing

allocated for R. H. Hardin

allocated

approved