login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A247586 Number of acute triangles with integer sides less than or equal to n. 4
1, 3, 6, 11, 17, 25, 36, 49, 64, 81, 102, 127, 154, 185, 219, 258, 301, 349, 401, 457, 520, 587, 660, 740, 824, 914, 1010, 1114, 1225, 1342, 1468, 1600, 1740, 1887, 2041, 2206, 2378, 2561, 2750, 2948 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..40.

Vladimir Letsko, Mathematical Marathon, problem 192 (in Russian).

EXAMPLE

a(2) = 3 because there are 3 acute triangles with integer sides less than or equal to 2: (1,1,1); (1,2,2); (2,2,2).

MAPLE

tr_a:=proc(n) local a, b, c, t, d; t:=0:

for a to n do

for b from a to n do

for c from b to min(a+b-1, n) do

d:=a^2+b^2-c^2:

if d>0 then t:=t+1 fi

od od od;

[n, t]; end;

MATHEMATICA

a[n_] := Module[{a, b, c, d, t = 0}, Do[d = a^2 + b^2 - c^2; If[d>0, t++], {a, n}, {b, a, n}, {c, b, Min[a+b-1, n]}]; t]; Array[a, 40] (* Jean-François Alcover, Jun 19 2019, from Maple *)

PROG

(Python)

import itertools

def A247586(n):

I = itertools.combinations_with_replacement(range(1, n+1), 3)

F = filter(lambda c: c[0]**2 + c[1]**2 > c[2]**2, I)

return len(list(F))

print([A247586(n) for n in range(41)]) # Peter Luschny, Sep 22 2014

CROSSREFS

Cf. A002623, A224921, A247587, A247588, A247589.

Sequence in context: A320272 A119639 A281376 * A107957 A000603 A003453

Adjacent sequences: A247583 A247584 A247585 * A247587 A247588 A247589

KEYWORD

nonn

AUTHOR

Vladimir Letsko, Sep 20 2014

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 20:59 EST 2022. Contains 358510 sequences. (Running on oeis4.)