The On-Line Encyclopedia of Integer Sequences (OEIS)

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A194136

T(n,k) = number of ways to arrange k indistinguishable points on an n X n X n triangular grid so that no three points are collinear at any angle.
(history; published version)

#8 by Joerg Arndt at Sat Dec 09 03:57:18 EST 2017

STATUS

proposed

approved

#7 by Jon E. Schoenfield at Sat Dec 09 03:35:22 EST 2017

STATUS

editing

proposed

#6 by Jon E. Schoenfield at Sat Dec 09 03:35:20 EST 2017

NAME

T(n,k) =Number number of ways to arrange k indistinguishable points on an nXnXn n X n X n triangular grid so that no three points are collinear at any angle.

EXAMPLE

Some solutions for n=4 , k=4:

CROSSREFS

Column 1 is A000217.

Column 2 is A050534.

AUTHOR

R. H. Hardin , Aug 17 2011

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:36:21 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Aug 17 2011

Discussion

Sat Mar 31

12:36

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

#4 by Ron Hardin at Wed Aug 17 09:59:11 EDT 2011

STATUS

editing

approved

#3 by Ron Hardin at Wed Aug 17 09:59:01 EDT 2011

LINKS

R. H. Hardin, <a href="/A194136/b194136.txt">Table of n, a(n) for n = 1..267</a>

#2 by Ron Hardin at Wed Aug 17 09:58:26 EDT 2011

NAME

allocated for Ron HardinT(n,k)=Number of ways to arrange k indistinguishable points on an nXnXn triangular grid so that no three points are collinear at any angle

DATA

1, 0, 3, 0, 3, 6, 0, 1, 15, 10, 0, 0, 17, 45, 15, 0, 0, 6, 105, 105, 21, 0, 0, 0, 114, 407, 210, 28, 0, 0, 0, 39, 843, 1216, 378, 36, 0, 0, 0, 1, 792, 4122, 3036, 630, 45, 0, 0, 0, 0, 244, 7587, 14988, 6696, 990, 55, 0, 0, 0, 0, 9, 6480, 43836, 45414, 13428, 1485, 66, 0, 0, 0, 0

OFFSET

1,3

COMMENTS

Table starts

...1....0......0.......0.........0..........0...........0............0

...3....3......1.......0.........0..........0...........0............0

...6...15.....17.......6.........0..........0...........0............0

..10...45....105.....114........39..........1...........0............0

..15..105....407.....843.......792........244...........9............0

..21..210...1216....4122......7587.......6480........1875...........78

..28..378...3036...14988.....43836......69798.......52323........14268

..36..630...6696...45414....194013.....496198......695616.......464934

..45..990..13428..119340....696765....2595897.....5840088......7278867

..55.1485..25005..281442...2145687...10912452....35715529.....71089536

..66.2145..43861..608616...5851044...38739354...172520643....496946172

..78.3003..73277.1228812..14546412..121694240...708871152...2796515883

..91.4095.117471.2338779..33347130..342722071..2517687856..12966188538

.105.5460.181880.4240284..71662911..887407361..8023634766..52262929401

.120.7140.273268.7371414.145616964.2136513884.23292994812.187041426756

EXAMPLE

Some solutions for n=4 k=4

.....1........0........1........0........0........0........0........0

....0.0......1.1......1.0......0.1......1.1......1.0......1.1......0.1

...0.1.0....0.0.1....0.0.0....1.0.0....1.0.0....1.0.1....1.1.0....1.1.0

..1.0.0.1..1.0.0.0..0.1.1.0..0.1.0.1..0.0.1.0..0.0.1.0..0.0.0.0..0.0.0.1

CROSSREFS

Column 1 is A000217

Column 2 is A050534

KEYWORD

allocated

nonn,tabl

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Aug 17 2011

STATUS

approved

editing

#1 by Ron Hardin at Wed Aug 17 09:44:15 EDT 2011

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved