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A189973
T(n,k)=Number of 3:4:5 proportioned triangles on a (n+1)X(k+1) grid
3
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 8, 16, 8, 0, 0, 0, 0, 12, 28, 28, 12, 0, 0, 0, 0, 16, 40, 48, 40, 16, 0, 0, 0, 0, 20, 56, 68, 68, 56, 20, 0, 0, 0, 0, 24, 72, 96, 96, 96, 72, 24, 0, 0, 0, 0, 28, 88, 124, 136, 136, 124, 88, 28, 0, 0, 0, 0, 32, 104, 152, 180, 192
OFFSET
1,18
COMMENTS
Table starts
.0.0..0...0...0...0...0...0...0...0...0....0....0....0....0....0....0....0....0
.0.0..0...0...0...0...0...0...0...0...0....0....0....0....0....0....0....0....0
.0.0..0...4...8..12..16..20..24..28..32...36...40...44...48...52...56...60...64
.0.0..4..16..28..40..56..72..88.104.120..136..152..168..184..200..216..232..248
.0.0..8..28..48..68..96.124.152.180.208..236..264..292..320..348..376..404..432
.0.0.12..40..68..96.136.180.224.268.316..364..412..460..508..556..604..652..700
.0.0.16..56..96.136.192.256.320.384.456..528..600..672..744..816..888..960.1032
.0.0.20..72.124.180.256.344.432.524.628..732..836..944.1052.1160.1268.1376.1484
.0.0.24..88.152.224.320.432.544.664.800..940.1080.1228.1380.1532.1684.1840.1996
.0.0.28.104.180.268.384.524.664.816.988.1168.1348.1540.1740.1940.2140.2348.2556
LINKS
FORMULA
Empirical for column k:
k=3: a(n) = 4*n - 12 for n>2
k=4: a(n) = 16*n - 56 for n>5
k=5: a(n) = 28*n - 100 for n>5
k=6: a(n) = 48*n - 212 for n>9
k=7: a(n) = 72*n - 336 for n>9
k=8: a(n) = 108*n - 568 for n>12
k=9: a(n) = 156*n - 968 for n>16
k=10: a(n) = 208*n - 1396 for n>16
k=11: a(n) = 264*n - 1844 for n>16
k=12: a(n) = 352*n - 2828 for n>23
k=13: a(n) = 444*n - 3856 for n>23
k=14: a(n) = 540*n - 4912 for n>23
EXAMPLE
Some solutions for n=7 k=5
..3..3....1..5....2..0....2..4....7..1....6..4....7..5....7..1....4..3....2..3
..3..0....1..1....2..4....2..0....3..1....3..4....4..5....4..1....0..3....2..0
..7..3....4..5....5..0....5..4....7..4....6..0....7..1....7..5....4..0....6..3
CROSSREFS
Sequence in context: A175372 A069191 A175362 * A282866 A098445 A290696
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin May 03 2011
STATUS
approved