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A208637
T(n,k)=Number of nXk 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors
11
1, 2, 2, 4, 5, 4, 8, 11, 13, 8, 16, 23, 32, 34, 16, 32, 47, 71, 95, 89, 32, 64, 95, 150, 225, 284, 233, 64, 128, 191, 309, 494, 722, 851, 610, 128, 256, 383, 628, 1042, 1652, 2331, 2552, 1597, 256, 512, 767, 1267, 2149, 3577, 5572, 7548, 7655, 4181, 512, 1024, 1535
OFFSET
1,2
COMMENTS
Table starts
...1....2....4.....8....16.....32.....64....128.....256.....512....1024
...2....5...11....23....47.....95....191....383.....767....1535....3071
...4...13...32....71...150....309....628...1267....2546....5105...10224
...8...34...95...225...494...1042...2149...4375....8840...17784...35687
..16...89..284...722..1652...3577...7504..15448...31440...63543..127884
..32..233..851..2331..5572..12404..26508..55260..113427..230559..465773
..64..610.2552..7548.18888..43284..94320.199299..412962..844943.1714680
.128.1597.7655.24476.64216.151656.337227.722733.1512764.3117620.6359210
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 4*a(n-1) -3*a(n-2)
k=4: a(n) = 5*a(n-1) -6*a(n-2) +a(n-3)
k=5: a(n) = 6*a(n-1) -10*a(n-2) +4*a(n-3)
k=6: a(n) = 7*a(n-1) -15*a(n-2) +10*a(n-3) -a(n-4)
k=7: a(n) = 8*a(n-1) -21*a(n-2) +20*a(n-3) -5*a(n-4)
Empirical for row n:
n=1: a(k)=2*a(k-1)
n=2: a(k)=3*a(k-1)-2*a(k-2)
n=3: a(k)=4*a(k-1)-5*a(k-2)+2*a(k-3)
n=4: a(k)=5*a(k-1)-9*a(k-2)+7*a(k-3)-2*a(k-4) for k>5
n=5: a(k)=6*a(k-1)-14*a(k-2)+16*a(k-3)-9*a(k-4)+2*a(k-5) for k>7
n=6: a(k)=7*a(k-1)-20*a(k-2)+30*a(k-3)-25*a(k-4)+11*a(k-5)-2*a(k-6) for k>9
n=7: a(k)=8*a(k-1)-27*a(k-2)+50*a(k-3)-55*a(k-4)+36*a(k-5)-13*a(k-6)+2*a(k-7) for k>11
EXAMPLE
Some solutions for n=4 k=3
..0..0..0....0..0..1....0..1..1....0..0..1....0..0..1....0..1..0....0..1..0
..1..1..0....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1
..0..1..1....0..1..0....0..1..0....0..1..0....1..0..0....0..1..0....1..0..1
..0..0..1....1..0..1....0..1..0....0..1..0....1..1..0....1..0..1....1..0..0
CROSSREFS
Column 2 is A001519(n+1)
Column 3 is A199109(n-1)
Row 2 is A052940(n-1)
Sequence in context: A286101 A072454 A115216 * A341867 A252938 A229402
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Feb 29 2012
STATUS
approved