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A207403
T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically
10
2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 12, 81, 102, 64, 10, 16, 144, 289, 216, 100, 12, 20, 256, 612, 729, 390, 144, 14, 25, 400, 1296, 1782, 1521, 636, 196, 16, 30, 625, 2340, 4356, 4212, 2809, 966, 256, 18, 36, 900, 4225, 8910, 11664, 8692, 4761, 1392, 324, 20, 42, 1296
OFFSET
1,1
COMMENTS
Table starts
..2...4....6....9....12.....16.....20.....25......30......36.......42.......49
..4..16...36...81...144....256....400....625.....900....1296.....1764.....2401
..6..36..102..289...612...1296...2340...4225....6890...11236....17066....25921
..8..64..216..729..1782...4356...8910..18225...33210...60516...101598...170569
.10.100..390.1521..4212..11664..26676..61009..123006..248004...456666...840889
.12.144..636.2809..8692..26896..68060.172225..380970..842724..1690038..3389281
.14.196..966.4761.16284..55696.154580.429025.1033590.2490084..5404650.11730625
.16.256.1392.7569.28362.106276.321110.970225.2529480.6594624.15405432.35988001
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*n
k=2: a(n) = 4*n^2
k=3: a(n) = 2*n^3 + 6*n^2 - 2*n
k=4: a(n) = n^4 + 6*n^3 + 7*n^2 - 6*n + 1
k=5: a(n) = (1/3)*n^5 + 3*n^4 + (28/3)*n^3 + 7*n^2 - (29/3)*n + 2
k=6: a(n) = (1/9)*n^6 + (4/3)*n^5 + (58/9)*n^4 + (40/3)*n^3 + (49/9)*n^2 - (44/3)*n + 4
k=7: a(n) = (1/36)*n^7 + (4/9)*n^6 + (53/18)*n^5 + (91/9)*n^4 + (589/36)*n^3 + (31/9)*n^2 - (58/3)*n + 6
EXAMPLE
Some solutions for n=4 k=3
..0..0..0....1..1..1....1..1..0....0..1..0....0..0..0....1..1..0....0..0..0
..1..0..0....1..1..1....1..0..1....1..1..0....0..1..0....0..0..0....0..1..0
..0..0..0....1..1..1....1..0..0....1..1..0....0..0..0....0..1..0....0..0..0
..0..0..0....1..1..1....1..0..1....1..1..0....0..0..0....0..1..0....0..1..0
CROSSREFS
Column 2 is A016742
Column 3 is A086113
Row 1 is A002620(n+2)
Row 2 is A030179(n+2)
Row 3 is A207118
Sequence in context: A081238 A333823 A207254 * A208142 A207024 A207169
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Feb 17 2012
STATUS
approved