A230840 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 upper left element zero

0, 0, 0, 0, 2, 0, 0, 22, 22, 0, 0, 162, 656, 162, 0, 0, 1202, 16496, 16496, 1202, 0, 0, 8974, 416540, 1361842, 416540, 8974, 0, 0, 66990, 10550264, 114297392, 114297392, 10550264, 66990, 0, 0, 500018, 267165468, 9617769208, 32002769030, 9617769208

Offset

1,5

Comments

Table starts

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

.0......2.........22............162...............1202...................8974

.0.....22........656..........16496.............416540...............10550264

.0....162......16496........1361842..........114297392.............9617769208

.0...1202.....416540......114297392........32002769030..........8988055879558

.0...8974...10550264.....9617769208......8988055879558.......8428081775041778

.0..66990..267165468...809092017194...2523446670940914....7899599586975791528

.0.500018.6765343878.68064007019810.708459022763836116.7404104956669952823022

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

k=2: a(n) = 8*a(n-1) -5*a(n-2) +8*a(n-3) -4*a(n-4)

k=3: [order 30] for n>31

Example

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

Crossrefs

Sequence in context: A244143 A066294 A363073 * A209454 A287713 A287785

Adjacent sequences: A230837 A230838 A230839 * A230841 A230842 A230843

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 31 2013

Status

approved