A123325 Number of distinct angles in all integer-sided triangles with all sides <= n.

1, 3, 9, 17, 35, 49, 82, 109, 149, 188, 262, 316, 419, 500, 607, 698, 876, 1004, 1222, 1383, 1589, 1782, 2108, 2318, 2634, 2914, 3253, 3564, 4088, 4411, 5000, 5392, 5917, 6410, 6995, 7468, 8308, 8926, 9661, 10268, 11313, 11976, 13136, 13951, 14875

Offset

1,2

Comments

Using the law of cosines, the angle A opposite side a has cos A = (b^2 + c^2 - a^2) / (2bc) and the cosine uniquely identifies an angle of a triangle.

Links

Table of n, a(n) for n=1..45.

Prog

(PARI) A123325(n)=local(i, j, k, l); r=0; l=listcreate(n^3); for(i=1, n, for(j=1, n, for(k=1, n, if(gcd(i, gcd(j, k))==1&&2*max(i, max(j, k))<i+j+k, listput(l, (j^2+k^2-i^2)/(2*j*k)))))); listsort(l, 1); matsize(Vec(l))[2]

Crossrefs

Cf. A123323, A123324.

Sequence in context: A049778 A270105 A294425 * A239206 A116688 A293423

Adjacent sequences: A123322 A123323 A123324 * A123326 A123327 A123328

Keyword

nonn

Author

Franklin T. Adams-Watters, Sep 25 2006

Status

approved