A241054 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

2, 3, 2, 4, 3, 4, 7, 2, 4, 6, 10, 10, 3, 6, 8, 15, 18, 24, 6, 8, 14, 24, 18, 60, 64, 6, 12, 20, 35, 46, 93, 163, 132, 15, 13, 30, 54, 58, 297, 280, 598, 690, 31, 20, 48, 83, 102, 507, 1423, 1392, 3411, 2142, 58, 28, 70, 124, 173, 1264, 4167, 10921, 13273, 11283, 7144, 170, 38

Offset: 1

Author

R. H. Hardin, Apr 15 2014

Keywords

• nonn
• tabl

Comments

Table starts

..2..3...4.....7......10........15..........24..........35..........54

..2..3...2....10......18........18..........46..........58.........102

..4..4...3....24......60........93.........297.........507........1264

..6..6...6....64.....163.......280........1423........4167.......13389

..8..8...6...132.....598......1392.......10921.......72769......370453

.14.12..15...690....3411.....13273......189680.....2667280....18820225

.20.13..31..2142...11283.....89910.....1511923....30914092...376386754

.30.20..58..7144...72578...1128052....35582068..1432670661.26960360814

.48.28.170.30662..404421..13331118...776191453.62057946683

.70.38.388.95669.2220973.128026529.14877945554

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..143

Crossrefs

Column 1 is A239851

Row 1 is A159288(n+1)

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-2) -a(n-4) +a(n-5) -a(n-7) +a(n-8) +a(n-11) for n>15

Empirical for row n:

n=1: a(n) = a(n-2) +2*a(n-3)

n=2: [order 15] for n>17

n=3: [order 70] for n>85