A239599 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or one 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, 4, 3, 10, 3, 4, 24, 15, 4, 7, 56, 64, 31, 4, 10, 132, 244, 187, 82, 5, 15, 312, 1030, 1310, 643, 177, 7, 24, 736, 4303, 9806, 8773, 1737, 458, 8, 35, 1736, 17923, 76769, 128347, 38824, 7461, 1071, 11, 54, 4096, 75264, 611126, 1991329, 1031560, 282333, 24946

Offset: 1

Author

R. H. Hardin, Mar 22 2014

Keywords

• nonn
• tabl

Comments

Table starts

..2..4....10.....24.......56........132.........312.........736........1736

..3..3....15.....64......244.......1030........4303.......17923.......75264

..4..4....31....187.....1310.......9806.......76769......611126.....4929897

..7..4....82....643.....8773.....128347.....1991329....31686730...510551001

.10..5...177...1737....38824....1031560....30460289...944810972.30050150163

.15..7...458...7461...282333...12509870...681399736.40483561185

.24..8..1071..24946..1583770..120511910.11135057785

.35.11..2150..78667..8002162.1104844380

.54.12..5209.313003.56967196

.83.16.11204.946740

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..95

Crossrefs

Column 1 is A159288(n+1)

Row 1 is A052912

Formula

Empirical for column k:

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

k=2: a(n) = a(n-2) +a(n-5) for n>6

Empirical for row n:

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

n=2: [order 44] for n>47