A024162 Number of incongruent integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 3, 2, 4, 2, 5, 4, 7, 4, 8, 6, 10, 6, 11, 9, 14, 9, 16, 12, 18, 12, 21, 15, 24, 16, 25, 20, 30, 19, 33, 25, 33, 25, 40, 28, 44, 30, 44, 36, 52, 34, 55, 42, 56, 42, 65, 44, 70, 49, 67, 56, 78, 52, 85, 64, 83, 63, 96, 66, 102, 72, 95, 81, 113, 75, 120, 88, 115, 90

Offset

1,13

References

A. M. Yaglom and I. M. Yaglom: Challenging Mathematical Problems with Elementary Solutions. Vol. I. Combinatorial Analysis and Probability Theory. New York: Dover Publications, Inc., 1987, p. 8, #30 (First published: San Francisco: Holden-Day, Inc., 1964)

Links

Table of n, a(n) for n=1..82.

Formula

For n=0..11 (mod 12), a(n) is respectively (n^2 + 6n - 7)/48, (n^2 - 4)/48, (n^2 + 6n + 21)/48, (n^2 - 16)/48, (n^2 + 6n - 7)/48, (n^2 + 12)/48, (n^2 + 6n + 5)/48, (n^2 - 16)/48, (n^2 + 6n + 9)/48, (n^2 - 4)/48, (n^2 + 6n + 5)/48

Crossrefs

Sequence in context: A308307 A147541 A308308 * A334677 A365876 A179080

Adjacent sequences: A024159 A024160 A024161 * A024163 A024164 A024165

Keyword

dead

Extensions

Apparently an erroneous version of A005044. For example a(18) should be 3 not 2.

Status

approved