A269937 T(n,k)=Number of nXk 0..6 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling six exactly once.

0, 7, 7, 84, 900, 84, 756, 36312, 36312, 756, 6048, 1213836, 5695536, 1213836, 6048, 45360, 36926640, 755009274, 755009274, 36926640, 45360, 326592, 1064495604, 91506078732, 399002850360, 91506078732, 1064495604, 326592, 2286144

Offset

1,2

Comments

Table starts

........0..............7...................84.......................756

........7............900................36312...................1213836

.......84..........36312..............5695536.................755009274

......756........1213836............755009274..............399002850360

.....6048.......36926640..........91506078732...........193171242190020

....45360.....1064495604.......10536802638018.........88942337408262936

...326592....29614748232.....1172354654705496......39591200828582988102

..2286144...803524526172...127313882431172946...17206536333078160595304

.15676416.21398721760608.13576906131836963556.7344924168583134203517654

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

k=1: a(n) = 12*a(n-1) -36*a(n-2)

k=2: [order 6] for n>7

k=3: [order 20] for n>21

k=4: [order 64] for n>65

Example

Some solutions for n=2 k=4
..0..3..1..6. .0..3..5..6. .0..0..0..5. .0..6..6..5. .0..2..2..6
..1..1..0..2. .3..5..6..3. .4..4..1..4. .3..5..2..6. .4..1..3..2

Crossrefs

Column 1 is A269895.

Sequence in context: A009201 A219353 A269902 * A065240 A178708 A072399

Adjacent sequences: A269934 A269935 A269936 * A269938 A269939 A269940

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 08 2016

Status

approved