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A207169
T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically
12
2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 13, 81, 90, 64, 10, 19, 169, 261, 168, 100, 12, 28, 361, 624, 603, 270, 144, 14, 41, 784, 1482, 1612, 1161, 396, 196, 16, 60, 1681, 3808, 3952, 3445, 1989, 546, 256, 18, 88, 3600, 9512, 11452, 8455, 6513, 3141, 720, 324, 20, 129, 7744
OFFSET
1,1
COMMENTS
Table starts
..2...4...6....9....13....19.....28.....41......60......88......129......189
..4..16..36...81...169...361....784...1681....3600....7744....16641....35721
..6..36..90..261...624..1482...3808...9512...23280...58080...144996...359100
..8..64.168..603..1612..3952..11452..32021...84300..231616...641775..1736910
.10.100.270.1161..3445..8455..26908..82861..228060..672760..2029041..5846337
.12.144.396.1989..6513.15789..54208.182081..515760.1608288..5222049.15774129
.14.196.546.3141.11284.26866..98224.357356.1032000.3365824.11680176.36617616
.16.256.720.4671.18304.42712.164668.645217.1888380.6392320.23581071.76187790
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*n
k=2: a(n) = 4*n^2
k=3: a(n) = 12*n^2 - 6*n
k=4: a(n) = 9*n^3 + 9*n - 9
k=5: a(n) = (13/4)*n^4 + (13/2)*n^3 + (117/4)*n^2 - 26*n
k=6: a(n) = (19/4)*n^4 + (95/2)*n^3 - (57/4)*n^2 - 19*n
k=7: a(n) = 35*n^4 + 42*n^3 + 7*n^2 - 84*n + 28
Empirical for rows:
n=1: a(k)=a(k-1)+a(k-3) for k>4
n=2: a(k)=a(k-1)+a(k-2)+3*a(k-3)+a(k-4)-a(k-5)-a(k-6) for k>7
n=3: a(k)=a(k-1)+9*a(k-3)+2*a(k-4)+2*a(k-5)-12*a(k-6)-8*a(k-7)+8*a(k-9) for k>11
n=4: a(k)=a(k-1)+13*a(k-3)+3*a(k-4)+3*a(k-5)-27*a(k-6)-18*a(k-7)+27*a(k-9) for k>11
n=5: a(k)=a(k-1)+17*a(k-3)+4*a(k-4)+4*a(k-5)-48*a(k-6)-32*a(k-7)+64*a(k-9) for k>11
n=6: a(k)=a(k-1)+21*a(k-3)+5*a(k-4)+5*a(k-5)-75*a(k-6)-50*a(k-7)+125*a(k-9) for k>11
n=7: a(k)=a(k-1)+25*a(k-3)+6*a(k-4)+6*a(k-5)-108*a(k-6)-72*a(k-7)+216*a(k-9) for k>11
n=8: a(k)=a(k-1)+29*a(k-3)+7*a(k-4)+7*a(k-5)-147*a(k-6)-98*a(k-7)+343*a(k-9) for k>11
n=9: a(k)=a(k-1)+33*a(k-3)+8*a(k-4)+8*a(k-5)-192*a(k-6)-128*a(k-7)+512*a(k-9) for k>11
n=10: a(k)=a(k-1)+37*a(k-3)+9*a(k-4)+9*a(k-5)-243*a(k-6)-162*a(k-7)+729*a(k-9) for k>11
n=11: a(k)=a(k-1)+41*a(k-3)+10*a(k-4)+10*a(k-5)-300*a(k-6)-200*a(k-7)+1000*a(k-9) for k>11
n=12: a(k)=a(k-1)+45*a(k-3)+11*a(k-4)+11*a(k-5)-363*a(k-6)-242*a(k-7)+1331*a(k-9) for k>11
n=13: a(k)=a(k-1)+49*a(k-3)+12*a(k-4)+12*a(k-5)-432*a(k-6)-288*a(k-7)+1728*a(k-9) for k>11
n=14: a(k)=a(k-1)+53*a(k-3)+13*a(k-4)+13*a(k-5)-507*a(k-6)-338*a(k-7)+2197*a(k-9) for k>11
n=15: a(k)=a(k-1)+57*a(k-3)+14*a(k-4)+14*a(k-5)-588*a(k-6)-392*a(k-7)+2744*a(k-9) for k>11
apparently a(k)=a(k-1)+(4*n-3)*a(k-3)+(n-1)*a(k-4)+(n-1)*a(k-5)-3*(n-1)^2*a(k-6)-2*(n-1)^2*a(k-7)+(n-1)^3*a(k-9) for n>2 and k>11
EXAMPLE
Some solutions for n=4 k=3
..1..0..0....0..0..1....0..1..1....1..1..1....0..0..1....1..0..0....1..0..0
..1..0..0....0..1..1....0..0..1....1..1..1....0..0..1....1..1..0....0..0..1
..1..0..0....0..1..0....0..0..1....1..1..1....0..0..1....0..1..0....0..0..1
..1..0..0....0..1..0....0..0..1....1..1..1....0..0..1....0..1..0....0..0..1
CROSSREFS
Column 2 is A016742
Column 3 is A152746
Row 1 is A000930(n+3)
Sequence in context: A207403 A208142 A207024 * A207111 A207305 A207391
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Feb 15 2012
STATUS
approved