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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A239851

Row 1 is A159288(n+1)

Sequence in context: A245134 A068962 A036380 * A257907 A139094 A159081

Adjacent sequences: A241051 A241052 A241053 * A241055 A241056 A241057

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 15 2014

Status

approved