

A020885


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


10



1, 5, 10, 14, 30, 35, 35, 55, 84, 91, 105, 140, 154, 165, 204, 220, 231, 260, 285, 286, 385, 390, 429, 455, 455, 506, 595, 650, 680, 715, 770, 819, 836, 935, 969, 1015, 1105, 1190, 1240, 1309, 1326, 1330, 1330, 1495, 1496, 1615, 1729, 1771, 1785, 1820, 1925
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OFFSET

1,2


COMMENTS

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
This sequence gives the area/6 (in some squared length unit) of primitive Pythagorean triangles with multiplicities modulo leg exchange. See the example.
This sequence also gives Fibonacci's congruous numbers divided by 24, with multiplicities and ordered nondecreasingly. See A258150.
(End)
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


LINKS



FORMULA



EXAMPLE

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


MATHEMATICA

Take[Sort[(Times@@#)/12&/@({Times@@#, (Last[#]^2First[#]^2)/2}&/@ Select[ Subsets[Range[1, 41, 2], {2}], GCD@@#==1&])], 60] (* Harvey P. Dale, Feb 27 2012 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



