A207254 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically.

2, 4, 4, 6, 16, 6, 8, 36, 36, 10, 10, 64, 102, 100, 16, 12, 100, 216, 370, 256, 26, 14, 144, 390, 940, 1232, 676, 42, 16, 196, 636, 1950, 3776, 4238, 1764, 68, 18, 256, 966, 3560, 9072, 15652, 14406, 4624, 110, 20, 324, 1392, 5950, 18688, 43498, 64176, 49164

Offset: 1

Author

R. H. Hardin Feb 16 2012

Keywords

• nonn
• tabl

Comments

Table starts

..2....4.....6......8.....10......12......14.......16.......18.......20

..4...16....36.....64....100.....144.....196......256......324......400

..6...36...102....216....390.....636.....966.....1392.....1926.....2580

.10..100...370....940...1950....3560....5950.....9320....13890....19900

.16..256..1232...3776...9072...18688...34608....59264....95568...146944

.26..676..4238..15652..43498..101036..207298...388232...677898..1119716

.42.1764.14406..64176.206514..541380.1231650..2524704..4777290..8483748

.68.4624.49164.263976.982940.2906592.7328836.16436824.33693660.64313720

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1057

Crossrefs

Column 1 is A006355(n+2)

Column 2 is A206981

Row 2 is A016742

Row 3 is A086113

Formula

Empirical for row n:

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

n=2: a(k) = 4*k^2

n=3: a(k) = 2*k^3 + 6*k^2 - 2*k

n=4: a(k) = (5/6)*k^4 + (35/3)*k^3 - (5/6)*k^2 - (5/3)*k

n=5: a(k) = (4/15)*k^5 + (32/3)*k^4 + (44/3)*k^3 - (32/3)*k^2 + (16/15)*k

n=6: a(k) = (13/180)*k^6 + (143/20)*k^5 + (1235/36)*k^4 - (39/4)*k^3 - (377/45)*k^2 + (13/5)*k

n=7: a(k) = (1/60)*k^7 + (77/20)*k^6 + (2527/60)*k^5 + (119/4)*k^4 - (644/15)*k^3 + (42/5)*k^2 + (4/5)*k