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A024153 Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n that have integer area. 6
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 3, 0, 0, 0, 2, 0, 1, 0, 1, 0, 2, 0, 3, 0, 0, 0, 1, 0, 1, 0, 3, 0, 0, 0, 8, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 4, 0, 3, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,36

COMMENTS

No such triangles with odd perimeter (see A051516).

Records occur at: 1, 12, 36, 54, 84, 108, 192, 216, 294, 324, 378, 420, 432, 540, 588, 756, 972, 1176, 1452, 1764, 1944, 2028, 2352, 2904, 2916, 3024, 3072, 3402, 3468, 3780, 3888, 4116, 5292, 6348, 6804, 8748, 10164, ... - Antti Karttunen, Sep 25 2018

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..12021 (terms 1..1000 from Seiichi Manyama)

Eric Weisstein's World of Mathematics, Heronian Triangle.

PROG

(PARI) A024153(n) = if(n%2, 0, my(k=0, t, p=n/2); for(a=1, n, for(b=1+max(a, (p-a)), n-(a+1), my(c=n-(a+b)); if((c<=b), break); if(((t = (p*(p-a)*(p-b)*(p-c))) > 0)&&issquare(t), k++))); (k)); \\ Antti Karttunen, Sep 25 2018

CROSSREFS

Cf. A051516, A070139, A070203, A188158, A301384.

Sequence in context: A070203 A070201 A070138 * A079127 A056674 A227761

Adjacent sequences:  A024150 A024151 A024152 * A024154 A024155 A024156

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

a(100) corrected by Seiichi Manyama, Sep 13 2018

STATUS

approved

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Last modified January 25 16:42 EST 2020. Contains 331245 sequences. (Running on oeis4.)