login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A279413 Triangle read by rows: T(n,k), n>=k>=1, is the number of isosceles triangles with integer coordinates that have a bounding box of size n X k. 10
0, 0, 4, 0, 2, 12, 0, 0, 6, 16, 0, 2, 4, 6, 24, 0, 0, 2, 8, 10, 28, 0, 2, 4, 2, 8, 6, 36, 0, 0, 2, 0, 6, 8, 10, 40, 0, 2, 4, 2, 12, 10, 8, 10, 56, 0, 0, 2, 4, 2, 4, 10, 8, 10, 60, 0, 2, 4, 2, 4, 2, 12, 6, 12, 6, 60, 0, 0, 2, 0, 2, 4, 6, 12, 6, 8, 14, 64, 0, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..9870 (the first 140 rows)

Lars Blomberg, Algorithms for computing A279413, A279414, A186434 and A271908

EXAMPLE

Triangle begins:

0

0, 4

0, 2, 12

0, 0, 6, 16

0, 2, 4, 6, 24

0, 0, 2, 8, 10, 28

0, 2, 4, 2, 8, 6, 36

0, 0, 2, 0, 6, 8, 10, 40

0, 2, 4, 2, 12, 10, 8, 10, 56

0, 0, 2, 4, 2, 4, 10, 8, 10, 60

0, 2, 4, 2, 4, 2, 12, 6, 12, 6, 60

0, 0, 2, 0, 2, 4, 6, 12, 6, 8, 14, 64

0, 2, 4, 2, 4, 6, 8, 10, 16, 14, 12, 14, 72

0, 0, 2, 0, 2, 4, 2, 8, 14, 4, 6, 12, 18, 76

0, 2, 4, 2, 4, 2, 8, 2, 8, 10, 16, 10, 12, 10, 84

0, 0, 2, 0, 6, 4, 2, 4, 6, 16, 6, 4, 10, 12, 14, 88

0, 2, 4, 2, 4, 2, 8, 2, 16, 6, 16, 10, 16, 6, 24, 10, 104

0, 0, 2, 0, 2, 0, 2, 4, 6, 4, 10, 12, 10, 12, 10, 12, 14, 100

0, 2, 4, 2, 4, 2, 12, 6, 4, 6, 12, 10, 20, 6, 12, 14, 16, 10, 124

0, 0, 2, 0, 2, 0, 2, 0, 2, 4, 6, 12, 10, 12, 10, 12, 18, 12, 10, 112

-----

Denote by 'o' the point adjacent to the two equal sides, and by 'x' the other two.

n=4, k=3:

...x  x...  .o..  ..o.  x...  ...x

o...  ...o  ...x  x...  ...x  x...

...x  x...  x...  ...x  .o..  ..o.

So T(4,3)=6.

-----

n=4,k=4:

o...  ...o  .x..  ..x.  o...  ...o  ..x.  .x..

...x  x...  ....  ....  ....  ....  ...x  x...

....  ....  ...x  x...  ...x  x...  ....  ....

.x..  ..x.  o...  ...o  ..x.  .x..  o...  ...o

-

...x  x...  x...  ...x  o..x  x..o  x...  ...x

.o..  ..o.  ....  ....  ....  ....  ....  ....

....  ....  .o..  ..o.  ....  ....  ....  ....

x...  ...x  ...x  x...  x...  ...x  o..x  x..o

So T(4,4)=16.

CROSSREFS

Cf. A186434, A187452, A271910-A271913, A271915, A279414.

See A279415 for right isosceles triangles.

See A280639 for obtuse isosceles triangles.

See A279418 for acute isosceles triangles.

See A279433 for all right triangles.

See A280652 for all obtuse triangles.

See A280653 for all acute triangles.

See A279432 for all triangles.

Sequence in context: A285750 A282279 A208333 * A208748 A134895 A318468

Adjacent sequences:  A279410 A279411 A279412 * A279414 A279415 A279416

KEYWORD

nonn,tabl

AUTHOR

Lars Blomberg, Feb 16 2017

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 December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)