A230686 T(n,k)=Number of nXk 0..6 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 7, and upper left element zero

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 68, 360, 32, 0, 0, 0, 0, 2, 1500, 24050, 15624, 432, 0, 0, 0, 0, 8, 18468, 974548, 2756394, 575280, 5182, 0, 0, 0, 0, 32, 199358, 30543988, 296568384, 272728160, 19355400, 58298, 0, 0, 0, 0

Offset

1,25

Comments

Table starts

.0.0.0.....0........0.........0.........0...........0.........0.......0...0.0

.0.0.0.....0........0.........0.........0...........2.........8......32.120

.0.0.0.....0........0........68......1500.......18468....199358.2097950

.0.0.0.....2......360.....24050....974548....30543988.887242598

.0.0.0....32....15624...2756394.296568384.24842737670

.0.0.0...432...575280.272728160

.0.0.0..5182.19355400

.0.0.0.58298

Links

R. H. Hardin, Table of n, a(n) for n = 1..71

Formula

Empirical for row n:

n=2: a(n) = 4*a(n-1) -4*a(n-3) -8*a(n-4) -12*a(n-5) -17*a(n-6) -10*a(n-7) for n>8

Empirical for column k:

k=4: [order 9]

k=5: [order 11] for n>12

Example

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

Crossrefs

Row 2 is A230529(n-1)

Sequence in context: A019261 A019222 A019141 * A341001 A221836 A279372

Adjacent sequences: A230683 A230684 A230685 * A230687 A230688 A230689

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 27 2013

Status

approved