A230831 T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero

0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 6, 8, 6, 0, 0, 16, 10, 10, 16, 0, 0, 44, 38, 62, 38, 44, 0, 0, 124, 130, 176, 176, 130, 124, 0, 0, 354, 456, 734, 898, 734, 456, 354, 0, 0, 1020, 1610, 3034, 4350, 4350, 3034, 1610, 1020, 0, 0, 2956, 5740, 12962, 22852, 29446, 22852, 12962

Offset

1,5

Comments

Table starts

.0...0....0.....0......0.......0........0.........0..........0...........0

.0...2....2.....6.....16......44......124.......354.......1020........2956

.0...2....8....10.....38.....130......456......1610.......5740.......20556

.0...6...10....62....176.....734.....3034.....12962......55806......241462

.0..16...38...176....898....4350....22852....122740.....661598.....3593650

.0..44..130...734...4350...29446...201592...1388526....9649244....67351066

.0.124..456..3034..22852..201592..1807682..16202418..145774974..1316654208

.0.354.1610.12962.122740.1388526.16202418.188719562.2198502114.25739337218

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

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

k=3: [order 12] for n>17

k=4: [order 46] for n>51

Example

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

Crossrefs

Sequence in context: A181111 A353856 A216800 * A230899 A230805 A230994

Adjacent sequences: A230828 A230829 A230830 * A230832 A230833 A230834

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 30 2013

Status

approved