A278188 T(n,k)=Number of nXk 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

0, 0, 0, 0, 3, 0, 0, 19, 28, 0, 0, 136, 544, 200, 0, 0, 935, 13012, 13720, 1532, 0, 0, 6381, 295190, 1075258, 347116, 11794, 0, 0, 43478, 6715738, 81691958, 91270219, 8803344, 90538, 0, 0, 296105, 152540636, 6196345742, 23124026160, 7737459027, 223230876

Offset

1,5

Comments

Table starts

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

.0.......3...........19..............136................935................6381

.0......28..........544............13012.............295190.............6715738

.0.....200........13720..........1075258...........81691958..........6196345742

.0....1532.......347116.........91270219........23124026160.......5858713218010

.0...11794......8803344.......7737459027......6545874548694....5537142857552112

.0...90538....223230876.....656008970388...1852662745588838.5232919178331757631

.0..695252...5660949042...55620335387114.524386828923495662

.0.5339294.143557203008.4715820197535009

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

k=2: a(n) = 8*a(n-1) -4*a(n-2) +15*a(n-3) -26*a(n-4) +14*a(n-5) -16*a(n-6)

k=3: [order 27]

Empirical for row n:

n=2: a(n) = 9*a(n-1) -16*a(n-2) +9*a(n-3) -12*a(n-4) +5*a(n-5) +7*a(n-6) -4*a(n-7)

n=3: [order 43]

Example

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

Crossrefs

Sequence in context: A291802 A221828 A368348 * A101192 A228622 A037288

Adjacent sequences: A278185 A278186 A278187 * A278189 A278190 A278191

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 14 2016

Status

approved