A269902 T(n,k)=Number of nXk 0..6 arrays with some element plus some horizontally or vertically adjacent neighbor totalling six exactly once.

0, 7, 7, 84, 840, 84, 756, 45360, 45360, 756, 6048, 2005080, 12377400, 2005080, 6048, 45360, 80724000, 2801265390, 2801265390, 80724000, 45360, 326592, 3078006120, 579818225700, 3263186052840, 579818225700, 3078006120, 326592, 2286144

Offset

1,2

Comments

Table starts

.....0..........7..............84.................756.....................6048

.....7........840...........45360.............2005080.................80724000

....84......45360........12377400..........2801265390.............579818225700

...756....2005080......2801265390.......3263186052840.........3482459146452300

..6048...80724000....579818225700....3482459146452300.....19179756370570398120

.45360.3078006120.113873466835170.3529041005211929340.100348236778061082424740

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

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

k=2: a(n) = 62*a(n-1) -961*a(n-2) for n>3

k=3: a(n) = 330*a(n-1) -28773*a(n-2) +255420*a(n-3) -599076*a(n-4) for n>5

k=4: [order 6] for n>7

k=5: [order 14] for n>15

k=6: [order 26] for n>27

Example

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

Crossrefs

Sequence in context: A274908 A009201 A219353 * A269937 A065240 A178708

Adjacent sequences: A269899 A269900 A269901 * A269903 A269904 A269905

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 07 2016

Status

approved