A230571 T(n,k)=Number of nXk 0..4 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 5, and upper left element zero

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 60, 32, 0, 0, 0, 0, 8, 868, 2582, 430, 0, 0, 0, 0, 32, 9088, 93450, 91084, 5130, 0, 0, 0, 0, 120, 94014, 2541242, 8554108, 3026090, 58474, 0, 0, 0, 0, 430, 952214, 70699812, 615786708, 765537650, 98987768

Offset

1,18

Comments

Table starts

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

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

.0.0.0......2.........60...........868.............9088................94014

.0.0.0.....32.......2582.........93450..........2541242.............70699812

.0.0.0....430......91084.......8554108........615786708..........45684933988

.0.0.0...5130....3026090.....765537650.....145982711348.......28811520101092

.0.0.0..58474...98987768...67978636208...34266592666538....17991771309348534

.0.0.0.651686.3223042422.6025699711838.8031211777081368.11220386097390449420

Links

R. H. Hardin, Table of n, a(n) for n = 1..125

Formula

Empirical for column k:

k=4: a(n) = 17*a(n-1) -66*a(n-2) -12*a(n-3) +13*a(n-4) +476*a(n-5) -44*a(n-6) +a(n-7)

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

k=6: [order 68] for n>69

Empirical for row n:

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

n=3: [order 48] for n>51

Example

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

Crossrefs

Row 2 is A230393(n-1)

Sequence in context: A297934 A112166 A112167 * A037213 A218234 A092197

Adjacent sequences: A230568 A230569 A230570 * A230572 A230573 A230574

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 23 2013

Status

approved