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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A159288(n+1)

Row 1 is A052912

Sequence in context: A157406 A075363 A082382 * A271864 A183210 A226367

Adjacent sequences: A239596 A239597 A239598 * A239600 A239601 A239602

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 22 2014

Status

approved