

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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
From Wolfdieter Lang, Jun 14 2015: (Start)
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)


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000
Ron Knott, Pythagorean Triples and Online Calculators


FORMULA

a(n) = A024406(n)/6.


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

Cf. A020882, A020883, A020884, A020886.
Sequence in context: A313665 A015847 A224692 * A258151 A280320 A213365
Adjacent sequences: A020882 A020883 A020884 * A020886 A020887 A020888


KEYWORD

nonn


AUTHOR

Clark Kimberling


EXTENSIONS

Extended and corrected by David W. Wilson


STATUS

approved



