The On-Line Encyclopedia of Integer Sequences (OEIS)

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A189973

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

#5 by Russ Cox at Sat Mar 31 12:36:19 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ May 03 2011

Discussion

Sat Mar 31

12:36

OEIS Server: https://oeis.org/edit/global/875

#4 by Ron Hardin at Tue May 03 06:58:45 EDT 2011

STATUS

proposed

approved

#3 by Ron Hardin at Tue May 03 06:58:25 EDT 2011

LINKS

R. H. Hardin, <a href="/A189973/b189973.txt">Table of n, a(n) for n = 1..10025</a>

#2 by Ron Hardin at Tue May 03 06:58:02 EDT 2011

NAME

allocated for Ron HardinT(n,k)=Number of 3:4:5 proportioned triangles on a (n+1)X(k+1) grid

DATA

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...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

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

KEYWORD

allocated

nonn,tabl

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) May 03 2011

STATUS

approved

proposed

#1 by Ron Hardin at Tue May 03 06:54:43 EDT 2011

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved