A186599 T(n,k) = Number of (n+3) X (k+3) 0..3 arrays with every 4 X 4 subblock commuting with each horizontal and vertical neighbor 4 X 4 subblock.

4294967296, 48243, 48243, 430183, 2703, 430183, 3306753, 8853, 8853, 3306753, 21993587, 104547, 33006, 104547, 21993587, 53301263, 444066, 407733, 407733, 444066, 53301263, 71095231, 884466, 1398069, 2526165, 1398069, 884466, 71095231

Offset

1,1

Comments

Table starts

.4294967296...48243..430183.3306753.21993587.53301263.71095231.78728809

......48243....2703....8853..104547...444066...884466..1126074..1184226

.....430183....8853...33006..407733..1398069..1824789..1889853..1922661

....3306753..104547..407733.2526165..5080629..5654805..5711805..5769381

...21993587..444066.1398069.5080629.11494293.12478581.12563805.12653493

...53301263..884466.1824789.5654805.12478581.16898709.17002221.17171973

...71095231.1126074.1889853.5711805.12563805.17002221.17395749.17856813

...78728809.1184226.1922661.5769381.12653493.17171973.17856813.20385141

...86748644.1210122.1956045.5831421.12809421.17632173.20158773.23590989

...89692007.1236594.1993893.5959701.13255797.19933269.23363757.27166341

Links

R. H. Hardin, Table of n, a(n) for n = 1..448

Formula

Empirical, for all columns: a(n) = 2*a(n-1)-a(n-2)+3*a(n-4)-6*a(n-5)+3*a(n-6)+3*a(n-8)-3*a(n-9) for n>30,14,13,14,15,16,17,18 respectively for k=1..8.

Example

Some solutions for 6 X 5
..0..0..3..1..1....0..0..1..1..3....0..0..1..2..2....0..0..0..0..1
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..2....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....2..0..0..0..0
..0..2..3..0..0....2..1..3..0..0....2..0..0..0..0....2..0..3..0..0

Crossrefs

Sequence in context: A244064 A255344 A186590 * A186591 A281576 A288282

Adjacent sequences: A186596 A186597 A186598 * A186600 A186601 A186602

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 24 2011

Status

approved