A278099 T(n,k)=Number of nXk 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

0, 0, 0, 0, 2, 0, 0, 10, 10, 0, 0, 58, 164, 58, 0, 0, 334, 2996, 2996, 334, 0, 0, 1910, 52310, 165408, 52310, 1910, 0, 0, 10910, 911096, 8817738, 8817738, 911096, 10910, 0, 0, 62314, 15854438, 469476315, 1432970150, 469476315, 15854438, 62314, 0, 0, 355898

Offset

1,5

Comments

Table starts

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

.0.......2..........10.............58..............334..............1910

.0......10.........164...........2996............52310............911096

.0......58........2996.........165408..........8817738.........469476315

.0.....334.......52310........8817738.......1432970150......232444783982

.0....1910......911096......469476315.....232444783982...114893826834782

.0...10910....15854438....24968293789...37664268929810.56727696580816184

.0...62314...275796494..1327640457829.6101731863309598

.0..355898..4797380865.70590643428412

.0.2032630.83447002829

Links

R. H. Hardin, Table of n, a(n) for n = 1..83

Formula

Empirical for column k:

k=2: a(n) = 6*a(n-1) -a(n-2) -3*a(n-3) -3*a(n-4) -6*a(n-5) +2*a(n-7)

k=3: [order 48] for n>49

Example

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

Crossrefs

Sequence in context: A010893 A181501 A213704 * A000171 A054922 A289651

Adjacent sequences: A278096 A278097 A278098 * A278100 A278101 A278102

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 12 2016

Status

approved