A332978 -id:A332978

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A333135

Irregular table read by rows: Take a triangle with Pythagorean triple leg lengths with all diagonals drawn, as in A332978. Then T(n,k) = number of k-sided polygons in that figure for k >= 3 where the legs are divided into unit length parts.

+20
4

139, 94, 34, 3, 1, 2383, 2421, 760, 167, 13, 2, 5307, 5958, 2113, 563, 80, 17, 2, 13083, 13560, 4479, 1002, 153, 16, 1, 18827, 20896, 8256, 2139, 377, 49, 6, 1, 42992, 45400, 15930, 3771, 579, 60, 5, 63526, 79275, 28922, 7315, 1404, 202, 14, 4

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

See A332978 for the Pythagorean triple ordering and the links for images of the triangles.

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..213 (the first 24 rows)

EXAMPLE

Table begins:

139, 94, 34, 3, 1;

2383, 2421, 760, 167, 13, 2;

5307, 5958, 2113, 563, 80, 17, 2;

13083, 13560, 4479, 1002, 153, 16, 1;

18827, 20896, 8256, 2139, 377, 49, 6, 1;

42992, 45400, 15930, 3771, 579, 60, 5;

63526, 79275, 28922, 7315, 1404, 202, 14, 4;

The row sums are A332978.

CROSSREFS

Cf. A332978 (regions), A333136 (vertices), A333137 (edges), A103605 (Pythagorean triple ordering), A007678, A092867, A331452.

KEYWORD

nonn,tabf

AUTHOR

Scott R. Shannon and N. J. A. Sloane, Mar 09 2020

EXTENSIONS

Corrected typo in a(12) and a(49) and beyond from Lars Blomberg, Jun 07 2020

STATUS

approved

A333136

The number of vertices formed on a triangle with leg lengths equal to the Pythagorean triples by the straight line segments mutually connecting all vertices and all points that divide the sides into unit length parts.

+10
3

230, 5138, 13181, 29277, 48107, 100003, 173261, 256910, 247940, 541752, 554717, 869197, 1051503, 987045, 1333241, 1190131, 1843049, 2991447, 3073340, 4382249, 4630456, 4635744, 5914142, 6877208

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

See A332978 for the Pythagorean triple ordering and the links for images of the triangles.

LINKS

Table of n, a(n) for n=1..24.

CROSSREFS

Cf. A332978 (regions), A333135 (n-gons), A333137 (edges), A103605 (Pythagorean triple ordering), A092866, A332599, A007569.

KEYWORD

nonn,more

AUTHOR

Scott R. Shannon and N. J. A. Sloane, Mar 09 2020

EXTENSIONS

a(8)-a(24) from Lars Blomberg, Jun 07 2020

STATUS

approved

A333137

The number of edges formed on a triangle with leg lengths equal to the Pythagorean triples by the straight line segments mutually connecting all vertices and all points that divide the sides into unit length parts.

+10
3

500, 10883, 27220, 61570, 98657, 208739, 353922, 533442, 507744, 1100007, 1146403, 1771007, 2168628, 2002321, 2719907, 2413390, 3787444, 6140737, 6238486, 8906032, 9394871, 9495582, 11939407, 14063303

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

See A332978 for the Pythagorean triple ordering and the links for images of the triangles.

LINKS

Table of n, a(n) for n=1..24.

CROSSREFS

Cf. A332978 (regions), A333135 (n-gons), A333136 (vertices), A103605 (Pythagorean triple ordering), A274586 , A332600, A331765.

KEYWORD

nonn,more

AUTHOR

Scott R. Shannon and N. J. A. Sloane, Mar 09 2020

EXTENSIONS

a(8)-a(24) from Lars Blomberg, Jun 07 2020

STATUS

approved

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