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

 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 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.

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