A190033 T(n,k)=Number of (n+2)X(k+2) binary arrays with every 3X3 subblock commuting with each horizontal and vertical neighbor 3X3 subblock

512, 112, 112, 228, 45, 228, 415, 79, 79, 415, 616, 155, 158, 155, 616, 880, 235, 274, 274, 235, 880, 1205, 295, 362, 458, 362, 295, 1205, 1508, 355, 430, 578, 578, 430, 355, 1508, 2008, 423, 506, 670, 834, 670, 506, 423, 2008, 2793, 531, 610, 790, 970, 970, 790

Offset

1,1

Comments

Table starts

..512.112..228..415..616..880.1205.1508.2008.2793..3776..5220..7274..9829.13345

..112..45...79..155..235..295..355..423..531..740..1037..1434..1992..2706..3628

..228..79..158..274..362..430..506..610..790.1094..1539..2128..2917..3951..5309

..415.155..274..458..578..670..790..966.1242.1702..2338..3247..4460..6025..8139

..616.235..362..578..834..970.1162.1418.1802.2446..3314..4446..6199..8432.11313

..880.295..430..670..970.1230.1494.1834.2338.3142..4226..5674..7686.10543.14268

.1205.355..506..790.1162.1494.1910.2362.3002.4006..5390..7234..9790.13178.17955

.1508.423..610..966.1418.1834.2362.3018.3834.5122..6886..9242.12530.16874.22626

.2008.531..790.1242.1802.2338.3002.3834.5102.6794..9110.12238.16562.22266.29874

.2793.740.1094.1702.2446.3142.4006.5122.6794.9706.12930.17246.23194.31074.41542

Links

R. H. Hardin, Table of n, a(n) for n = 1..5196

Formula

Empirical for all columns: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5) +a(n-6) -a(n-7) for n>11,10,11,12,13,14,15,16 respectively for k=1..8

Example

Some solutions for 5X4
..0..0..0..1....0..0..0..1....0..0..1..1....0..0..1..1....1..1..1..1
..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
..1..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..1..1..0..0....0..0..0..0....0..0..0..1....0..0..0..0....1..1..1..1

Crossrefs

Sequence in context: A351249 A190024 A376951 * A190025 A077743 A111447

Adjacent sequences: A190030 A190031 A190032 * A190034 A190035 A190036

Keyword

nonn,tabl

Author

R. H. Hardin May 04 2011

Status

approved