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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
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Jan 25 2012
STATUS
approved