A230915 T(n,k)=Number of nXk 0..7 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 8, and upper left element zero

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, 0, 0, 0, 0, 8, 164, 118, 0, 0, 0, 0, 32, 1650, 5714, 1506, 0, 0, 0, 0, 118, 17694, 154352, 221768, 20028, 0, 0, 0, 0, 440, 200654, 4725576, 16515468, 9144134, 271450, 0, 0, 0, 0, 1664, 2327434, 148720522

Offset

1,17

Comments

Table starts

.0.0.0.......0...........0..............0...............0...............0

.0.0.0.......0...........2..............8..............32.............118

.0.0.0.......8.........164...........1650...........17694..........200654

.0.0.0.....118........5714.........154352.........4725576.......148720522

.0.0.0....1506......221768.......16515468......1406791226....123455818582

.0.0.0...20028.....9144134.....1821132074....433315174684.107053049550326

.0.0.0..271450...372256436...198872246508.132452949993492

.0.0.0.3678640.15083831290.21679064102116

Links

R. H. Hardin, Table of n, a(n) for n = 1..95

Formula

Empirical for column k:

k=4: a(n) = 18*a(n-1) -91*a(n-2) +469*a(n-3) -919*a(n-4) +2152*a(n-5) -93*a(n-6) +a(n-7)

k=5: [order 9] for n>10

Empirical for row n:

n=2: a(n) = 5*a(n-1) -4*a(n-2) -5*a(n-3) +9*a(n-4) +12*a(n-5) for n>6

n=3: [order 49] for n>52

Example

Some solutions for n=3 k=4
..0..1..0..7....0..1..0..7....0..1..2..1....0..1..2..3....0..1..2..3
..2..3..6..5....2..3..6..3....2..3..0..7....0..1..4..5....0..7..4..3
..4..5..4..3....4..5..4..3....4..5..6..5....0..7..6..5....6..5..2..1

Crossrefs

Row 2 is A230509(n-1)

Sequence in context: A050809 A246516 A095217 * A242922 A242530 A073410

Adjacent sequences: A230912 A230913 A230914 * A230916 A230917 A230918

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 01 2013

Status

approved