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A070109 Number of right integer triangles with perimeter n and relatively prime side lengths. 13
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1716

COMMENTS

Right integer triangles have integer areas: see A070142, A051516.

a(n) is nonzero iff n is in A024364.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000 (obtained from the b-file of A078926)

Eric Weisstein's World of Mathematics, Right Triangle.

Eric Weisstein's World of Mathematics, Pythagorean Triples.

R. Zumkeller, Integer-sided triangles

FORMULA

a(n) = A078926(n/2) if n is even; a(n)=0 if n is odd.

a(n) = A051493(n) - A070094(n) - A070102(n).

a(n) <= A024155(n).

EXAMPLE

For n=30 there are A005044(30) = 19 integer triangles; only one is right: 5+12+13 = 30, 5^2+12^2 = 13^2; therefore a(30) = 1.

CROSSREFS

Cf. A070080, A070081, A070082, A051493, A070093, A070101, A070138, A070084, A070137.

Sequence in context: A277163 A011726 A297041 * A107846 A179801 A065202

Adjacent sequences:  A070106 A070107 A070108 * A070110 A070111 A070112

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 05 2002

EXTENSIONS

Secondary offset added by Antti Karttunen, Oct 07 2017

STATUS

approved

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Last modified February 15 22:28 EST 2019. Contains 320138 sequences. (Running on oeis4.)