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

Author

R. H. Hardin, Nov 14 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

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]