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

Author

R. H. Hardin Jan 25 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A115099.

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)