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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 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

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