A205318 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

8, 20, 20, 56, 84, 56, 164, 376, 376, 164, 488, 1708, 2606, 1708, 488, 1460, 7784, 18152, 18152, 7784, 1460, 4376, 35500, 126536, 193664, 126536, 35500, 4376, 13124, 161928, 882182, 2068148, 2068148, 882182, 161928, 13124, 39368, 738636, 6150512

Offset

1,1

Comments

Table starts

.....8.....20.......56........164..........488..........1460............4376

....20.....84......376.......1708.........7784.........35500..........161928

....56....376.....2606......18152.......126536........882182.........6150512

...164...1708....18152.....193664......2068148......22091516.......235994088

...488...7784...126536....2068148.....33865634.....554916092......9094954742

..1460..35500...882182...22091516....554916092...13956665238....351210375464

..4376.161928..6150512..235994088...9094954742..351210375464..13574876544398

.13124.738636.42881096.2521075824.149077423220.8839958693704.524918733085720

Links

R. H. Hardin, Table of n, a(n) for n = 1..420

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -3*a(n-2)

k=2: a(n) = 6*a(n-1) -7*a(n-2) +2*a(n-3)

k=3: a(n) = 10*a(n-1) -24*a(n-2) +21*a(n-3) -6*a(n-4)

k=4: a(n) = 17*a(n-1) -81*a(n-2) +157*a(n-3) -140*a(n-4) +56*a(n-5) -8*a(n-6)

k=5: a(n) = 31*a(n-1) -321*a(n-2) +1569*a(n-3) -4179*a(n-4) +6420*a(n-5) -5671*a(n-6) +2668*a(n-7) -516*a(n-8)

k=6: (order 14 recurrence)

k=7: (order 20 recurrence)

Example

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

Crossrefs

Column 1 is A115099.

Sequence in context: A022700 A214457 A205226 * A100212 A349168 A083094

Adjacent sequences: A205315 A205316 A205317 * A205319 A205320 A205321

Keyword

nonn,tabl

Author

R. H. Hardin Jan 25 2012

Status

approved