login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A298121 a(n) is the number of triangles (up to congruence) with integer coordinates that have perimeter strictly less than n. 2
1, 3, 5, 11, 18, 29, 44, 70, 94, 136, 177, 243, 303, 386, 485, 611, 738, 914, 1093, 1312, 1529, 1831, 2114, 2488, 2854, 3310, 3756, 4307, 4880, 5520, 6187, 6995, 7800, 8738, 9674, 10797, 11875, 13161, 14437, 15901, 17388, 19087, 20797, 22706, 24618, 26811 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

Peter Kagey, Table of n, a(n) for n = 4..150

Peter Kagey, Integer Triangles with perimeter less than n, Programming Puzzles & Code Golf Stack Exchange.

FORMULA

a(n) = Sum_{k=3..n-1} A298079(k).

EXAMPLE

All a(7) = 11 triangles with integer coordinates and perimeter less than 7 are congruent to triangles with coordinates:

(0, 0), (0, 1), (1, 0) - with perimeter ~3.41; or

(0, 0), (1, 2), (0, 1) - with perimeter ~4.65; or

(0, 0), (0, 2), (1, 1) - with perimeter ~4.82; or

(0, 0), (0, 2), (1, 0) - with perimeter ~5.23; or

(0, 0), (1, 2), (2, 1) - with perimeter ~5.88; or

(0, 0), (2, 2), (0, 1) - with perimeter ~6.06; or

(0, 0), (1, 3), (0, 1) - with perimeter ~6.39; or

(0, 0), (0, 2), (2, 1) - with perimeter ~6.47; or

(0, 0), (1, 3), (0, 2) - with perimeter ~6.57; or

(0, 0), (0, 3), (1, 1) - with perimeter ~6.65; or

(0, 0), (0, 2), (2, 0) - with perimeter ~6.82.

CROSSREFS

Cf. A298079.

Sequence in context: A267030 A128949 A070316 * A244473 A023597 A281357

Adjacent sequences:  A298118 A298119 A298120 * A298122 A298123 A298124

KEYWORD

nonn

AUTHOR

Peter Kagey, Jan 12 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 8 02:27 EDT 2020. Contains 333312 sequences. (Running on oeis4.)