A222169 T(n,k)=Number of nXk 0..4 arrays with entries increasing mod 5 by 0, 1 or 2 rightwards and downwards, starting with upper left zero.

1, 3, 3, 9, 19, 9, 27, 121, 121, 27, 81, 771, 1665, 771, 81, 243, 4913, 22979, 22979, 4913, 243, 729, 31307, 317259, 690437, 317259, 31307, 729, 2187, 199497, 4380445, 20780181, 20780181, 4380445, 199497, 2187, 6561, 1271251, 60481881, 625649047

Offset: 1

Author

R. H. Hardin Feb 10 2013

Keywords

• nonn
• tabl

Comments

Table starts

......1..........3..............9.................27.....................81

......3.........19............121................771...................4913

......9........121...........1665..............22979.................317259

.....27........771..........22979.............690437...............20780181

.....81.......4913.........317259...........20780181.............1366395515

....243......31307........4380445..........625649047............89948464453

....729.....199497.......60481881........18838482047..........5923189816253

...2187....1271251......835088891.......567241901289........390086038882651

...6561....8100769....11530288395.....17080173559277......25690815631493191

..19683...51620379...159201677509....514300085627023....1691995329032459285

..59049..328939577..2198138788809..15486061794514775..111434983000652039093

.177147.2096095523.30350271502115.466299978310573033.7339124863989795685471

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..180

Crossrefs

Diagonal is A068748

Column 1 is A000244(n-1)

Column 2 is A138977

Column 3 is A138978

Column 4 is A138979

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1)

k=2: a(n) = 7*a(n-1) -4*a(n-2)

k=3: a(n) = 16*a(n-1) -31*a(n-2) +10*a(n-3)

k=4: [order 10]

k=5: [order 25]

k=6: [order 70]