A307828 Number of integer-sided triangles with perimeter n whose smallest side-length divides n.

0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 4, 3, 1, 3, 1, 5, 4, 1, 1, 8, 4, 1, 4, 6, 1, 8, 1, 7, 4, 1, 8, 12, 1, 1, 4, 14, 1, 9, 1, 8, 12, 1, 1, 18, 5, 8, 4, 9, 1, 10, 10, 17, 4, 1, 1, 28, 1, 1, 13, 15, 11, 11, 1, 11, 4, 18, 1, 31, 1, 1, 15, 12, 11, 12, 1, 32

Offset: 1

Author

Wesley Ivan Hurt, May 15 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10220
• Wikipedia, Integer Triangle

Crossrefs

Cf. A005044.

Programs

Mathematica

Table[Sum[Sum[(1 - Ceiling[n/k] + Floor[n/k]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

PARI

A307828(n) = sum(k=1, n\3, sum(i=k, (n-k)\2, sign(floor((i+k)/(n-i-k+1)) * (1 - ceil(n/k) + floor(n/k))))); \\ Antti Karttunen, Dec 05 2021

Formula

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1)) * (1 - ceiling(n/k) + floor(n/k))).