The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A320543

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A320543

(1/2) * number of ways to select 3 distinct points forming a triangle of unsigned area = 1 from a rectangle of grid points with side lengths j and k, written as triangle T(j,k), j<=k.
(history; published version)

#10 by Susanna Cuyler at Mon Oct 22 14:28:46 EDT 2018

STATUS

proposed

approved

#9 by Hugo Pfoertner at Mon Oct 22 14:10:18 EDT 2018

STATUS

editing

proposed

#8 by Hugo Pfoertner at Mon Oct 22 14:06:40 EDT 2018

NAME

(1/2) * number of ways to select 3 distinct points forming a triangle of unsigned area = 1 from a rectangle of grid points with side lengths j and k, written as triangle T(j,k), j<=k.

#7 by Hugo Pfoertner at Mon Oct 22 13:09:54 EDT 2018

EXAMPLE

(0 ,0) (0 ,2) (1 ,0),

(0 ,0) (0 ,2) (1 ,1),

(0 ,0) (0 ,2) (1 ,2),

(0 ,0) (1 ,0) (1 ,2),

(0 ,1) (1 ,0) (1 ,2),

(0 ,2) (1 ,0) (1 ,2).

#6 by Hugo Pfoertner at Mon Oct 22 13:06:46 EDT 2018

DATA

0, 3, 16, 8, 35, 72, 15, 62, 125, 212, 24, 95, 190, 319, 476, 35, 136, 269, 450, 669, 936, 56, 48, 183, 360, 601, 892, 1245, 1652, 63, 238, 467, 776, 1149, 1602, 2123, 2724, 80, 299, 584, 967, 1430, 1991, 2636, 3379, 4188, 99, 368, 717, 1186, 1751, 2436, 3223, 4130, 5117, 6248

#5 by Hugo Pfoertner at Mon Oct 22 13:00:47 EDT 2018

EXAMPLE

The triangle begins:

0

3 16

8 35 72

15 62 125 212

24 95 190 319 476

35 136 269 450 669 936

.

a(2) = T(1,2) = 3 = 6/2 because the following 6 triangles of area 1 can be made by selecting 3 grid points from the [0,1]X[0,2] rectangle:

(0 0) (0 2) (1 0),

(0 0) (0 2) (1 1),

(0 0) (0 2) (1 2),

(0 0) (1 0) (1 2),

(0 1) (1 0) (1 2),

(0 2) (1 0) (1 2).

#4 by Hugo Pfoertner at Tue Oct 16 17:03:05 EDT 2018

CROSSREFS

Cf. A005562. A005563, A320539, A320541, A320544.

#3 by Hugo Pfoertner at Tue Oct 16 16:41:53 EDT 2018

CROSSREFS

Cf. A005562. A320539, A320541, A320544.

#2 by Hugo Pfoertner at Tue Oct 16 16:36:11 EDT 2018

NAME

allocated for Hugo Pfoertner(1/2) * number of ways to select 3 distinct points forming a triangle of unsigned area=1 from a rectangle of grid points with side lengths j and k, written as triangle T(j,k), j<=k.

DATA

0, 3, 16, 8, 35, 72, 15, 62, 125, 212, 24, 95, 190, 319, 476, 35, 136, 269, 450, 669, 936, 56, 183, 360, 601, 892, 1245, 1652, 63, 238, 467, 776, 1149, 1602, 2123, 2724, 80, 299, 584, 967, 1430, 1991, 2636, 3379, 4188, 99, 368, 717, 1186, 1751, 2436, 3223, 4130, 5117, 6248

OFFSET

1,2

CROSSREFS

Cf. A320539, A320541, A320544.

KEYWORD

allocated

nonn,tabl

AUTHOR

Hugo Pfoertner, Oct 16 2018

STATUS

approved

editing

#1 by Hugo Pfoertner at Mon Oct 15 10:13:04 EDT 2018

NAME

allocated for Hugo Pfoertner

KEYWORD

allocated

STATUS

approved