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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A006355(n+2)

Column 2 is A206981

Row 2 is A016742

Row 3 is A086113

Sequence in context: A276985 A081238 A333823 * A207403 A208142 A207024

Adjacent sequences: A207251 A207252 A207253 * A207255 A207256 A207257

Keyword

nonn,tabl

Author

R. H. Hardin Feb 16 2012

Status

approved