A208379 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

2, 4, 4, 6, 16, 6, 10, 36, 36, 8, 16, 100, 72, 64, 10, 26, 256, 240, 108, 100, 12, 42, 676, 704, 420, 144, 144, 14, 68, 1764, 2080, 1344, 640, 180, 196, 16, 110, 4624, 6216, 4212, 2176, 900, 216, 256, 18, 178, 12100, 18496, 13860, 7072, 3200, 1200, 252, 324, 20, 288

Offset: 1

Author

R. H. Hardin Feb 25 2012

Keywords

• nonn
• tabl

Comments

Table starts

..2...4...6...10...16....26....42.....68.....110.....178......288......466

..4..16..36..100..256...676..1764...4624...12100...31684....82944...217156

..6..36..72..240..704..2080..6216..18496...55000..163760...487296..1450192

..8..64.108..420.1344..4212.13860..44880..144540..468852..1517184..4906980

.10.100.144..640.2176..7072.25200..87040..296560.1028128..3545856.12198016

.12.144.180..900.3200.10660.40740.148240..526900.1931300..7015680.25336420

.14.196.216.1200.4416.14976.60984.231744..851400.3276624.12438144.46737936

.16.256.252.1540.5824.20020.86436.340816.1285900.5170900.20393856.79220932

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1463

Crossrefs

Column 1 is A004275(n+1)

Column 2 is A016742

Column 3 is A044102(n-1) for n>1

Row 1 is A006355(n+2)

Row 2 is A206981

Row 3 is A207840

Formula

Empirical for column k:

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

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

k=3: a(n) = 36*n - 36 for n>1

k=4: a(n) = 20*n^2 + 40*n - 60 for n>1

k=5: a(n) = 96*n^2 - 32*n - 64 for n>1

k=6: a(n) = 364*n^2 - 416*n + 52 for n>1

k=7: a(n) = 84*n^3 + 840*n^2 - 1344*n + 420 for n>1

Empirical for row n:

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

n=2: a(k)=2*a(k-1)+2*a(k-2)-a(k-3)

n=3: a(k)=a(k-1)+4*a(k-2)+5*a(k-3)+2*a(k-4)-a(k-5)+a(k-6) for k>8

n=4: a(k)=a(k-1)+4*a(k-2)+9*a(k-3)+5*a(k-4)-2*a(k-5)+4*a(k-6) for k>8

n=5: a(k)=a(k-1)+4*a(k-2)+13*a(k-3)+8*a(k-4)-3*a(k-5)+9*a(k-6) for k>8

n=6: a(k)=a(k-1)+4*a(k-2)+17*a(k-3)+11*a(k-4)-4*a(k-5)+16*a(k-6) for k>8

n=7: a(k)=a(k-1)+4*a(k-2)+21*a(k-3)+14*a(k-4)-5*a(k-5)+25*a(k-6) for k>8