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

1,1

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

Links

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

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

Example

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

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

Sequence in context: A208698 A207928 A207858 * A207453 A208287 A208501

Adjacent sequences: A208376 A208377 A208378 * A208380 A208381 A208382

Keyword

nonn,tabl

Author

R. H. Hardin Feb 25 2012

Status

approved