cp's OEIS Frontend

A020885 Ordered areas (divided by 6) of primitive Pythagorean triangles (with multiple entries).

%I A020885 #38 May 12 2022 12:19:20
%S A020885 1,5,10,14,30,35,35,55,84,91,105,140,154,165,204,220,231,260,285,286,
%T A020885 385,390,429,455,455,506,595,650,680,715,770,819,836,935,969,1015,
%U A020885 1105,1190,1240,1309,1326,1330,1330,1495,1496,1615,1729,1771,1785,1820,1925
%N A020885 Ordered areas (divided by 6) of primitive Pythagorean triangles (with multiple entries).
%C A020885 Since squares are 0 or 1 under both mod 3 and mod 4, for the Pythagorean equation A^2 + B^2 = C^2 to hold, each of 3 and 4 divides either of leg A or leg B, so that area A*B/2 is divisible by 3*4/2 = 6. - _Lekraj Beedassy_, Apr 30 2004
%C A020885 From _Wolfdieter Lang_, Jun 14 2015: (Start)
%C A020885 This sequence gives the area/6 (in some squared length unit) of primitive Pythagorean triangles with multiplicities modulo leg exchange. See the example.
%C A020885 This sequence also gives Fibonacci's congruous numbers divided by 24, with multiplicities and ordered nondecreasingly. See A258150.
%C A020885 (End)
%C A020885 It appears that this sequence gives the list of dimensions of irreducible unitary representations of the Lie group SO(5). - _Antoine Bourget_, Mar 30 2022
%H A020885 Giovanni Resta, <a href="/A020885/b020885.txt">Table of n, a(n) for n = 1..10000</a>
%H A020885 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html">Pythagorean Triples and Online Calculators</a>
%F A020885 a(n) = A024406(n)/6.
%e A020885 a(6) = a(7) = 35 from the two Pythagorean triangles (A,B,C) = (21, 20, 29)  and (35, 12, 37) with area 210. Triangles (20, 21, 29) and (12, 35, 37) are not counted (leg exchange). - _Wolfdieter Lang_, Jun 14 2015
%t A020885 Take[Sort[(Times@@#)/12&/@({Times@@#,(Last[#]^2-First[#]^2)/2}&/@ Select[ Subsets[Range[1,41,2],{2}],GCD@@#==1&])],60] (* _Harvey P. Dale_, Feb 27 2012 *)
%Y A020885 Cf. A020882, A020883, A020884, A020886.
%K A020885 nonn
%O A020885 1,2
%A A020885 _Clark Kimberling_
%E A020885 Extended and corrected by _David W. Wilson_