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A070086 Areas of integer triangles [A070080(n), A070081(n), A070082(n)], rounded values. 13
0, 1, 2, 1, 2, 3, 2, 3, 4, 4, 4, 2, 4, 4, 6, 5, 6, 7, 3, 5, 5, 7, 8, 6, 7, 8, 9, 3, 6, 6, 9, 7, 10, 11, 7, 9, 10, 11, 12, 4, 6, 8, 10, 8, 12, 12, 14, 8, 10, 12, 13, 12, 15, 16, 4, 7, 9, 12, 10, 14, 10, 15, 16, 17, 9, 12, 13, 15, 14, 17, 18, 19, 5, 8, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Triangles [A070080(A070142(n)), A070081(A070142(n)), A070082(A070142(n))] have integer areas = a(A070142(k)) = A070149(k).

LINKS

Table of n, a(n) for n=1..75.

Eric Weisstein's World of Mathematics, Heron's Formula.

R. Zumkeller, Integer-sided triangles

FORMULA

a(n) = sqrt(s*(s-u)*(s-v)*(s-w)), where u=A070080(n), v=A070081(n), w=A070082(n) and s = A070083(n)/2 = (u+v+w)/2.

EXAMPLE

[A070080(25), A070081(25), A070082(25)] = [3,5,6] and s = A070083(25)/2 = (3+5+6)/2 = 7: a(25) = sqrt(s*(s-3)*(s-5)*(s-6)) = sqrt(7*(7-3)*(7-5)*(7-6)) = sqrt(7*4*2*1) = sqrt(56) = 7.48331, rounded = 7.

CROSSREFS

Cf. A051516, A055595, A069596, A069594, A046131.

Sequence in context: A008611 A025798 A161064 * A211990 A162618 A036576

Adjacent sequences:  A070083 A070084 A070085 * A070087 A070088 A070089

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 05 2002

STATUS

approved

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Last modified February 24 11:12 EST 2018. Contains 299603 sequences. (Running on oeis4.)