A189973 T(n,k)=Number of 3:4:5 proportioned triangles on a (n+1)X(k+1) grid

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

R. H. Hardin, Table of n, a(n) for n = 1..10025

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

Adjacent sequences: A189970 A189971 A189972 * A189974 A189975 A189976

Keyword

nonn,tabl

Author

R. H. Hardin May 03 2011

Status

approved