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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-Fran├žois 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

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Last modified June 29 18:25 EDT 2022. Contains 354913 sequences. (Running on oeis4.)