A240321 T(n,k)=Number of nXk 0..3 arrays with no element equal to two plus the sum of elements to its left or two plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest, modulo 4

2, 2, 2, 4, 4, 4, 4, 18, 18, 4, 8, 44, 172, 44, 8, 8, 184, 866, 866, 184, 8, 16, 444, 7326, 8456, 7326, 444, 16, 16, 1826, 35042, 143682, 143682, 35042, 1826, 16, 32, 4388, 291982, 1352558, 4934092, 1352558, 291982, 4388, 32, 32, 18022, 1387224, 22643786

Offset

1,1

Comments

Table starts

..2.....2........4...........4..............8...............8...............16

..2.....4.......18..........44............184.............444.............1826

..4....18......172.........866...........7326...........35042...........291982

..4....44......866........8456.........143682.........1352558.........22643786

..8...184.....7326......143682........4934092........92600224.......3120733284

..8...444....35042.....1352558.......92600224......3462370700.....233738937688

.16..1826...291982....22643786.....3120733284....233738937688...31675283550406

.16..4388..1387224...211572262....58052954898...8672268288766.2350783897073214

.32.18022.11520638..3529400774..1946100075968.582902538705858

.32.43300.54650290.32917918872.36103692985126

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

Formula

Empirical for column k:

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

k=2: a(n) = 12*a(n-2) -24*a(n-4) +31*a(n-6) -16*a(n-8)

k=3: [order 48]

Example

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

Crossrefs

Column 1 is A016116(n+1)

Sequence in context: A369207 A113402 A238726 * A054861 A187324 A334207

Adjacent sequences: A240318 A240319 A240320 * A240322 A240323 A240324

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 03 2014

Status

approved