A308167 Number of integer-sided triangles with perimeter n and sides a, b, and c such that a <= b <= c and a|b.

0, 0, 1, 0, 1, 1, 2, 0, 2, 2, 3, 1, 2, 2, 5, 2, 3, 3, 4, 2, 5, 5, 6, 2, 4, 4, 7, 5, 6, 6, 7, 3, 6, 6, 9, 6, 7, 7, 10, 6, 7, 7, 8, 6, 11, 11, 12, 6, 8, 8, 11, 9, 10, 10, 13, 9, 12, 12, 13, 9, 10, 10, 15, 10, 13, 13, 14, 12, 15, 15, 16, 10, 11, 11, 16, 14, 17

Offset

1,7

Links

Table of n, a(n) for n=1..77.

Wikipedia, Integer Triangle

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(i/k) + floor(i/k)).

Mathematica

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

Crossrefs

Cf. A308166.

Sequence in context: A144741 A352965 A103615 * A293665 A159632 A164733

Adjacent sequences: A308164 A308165 A308166 * A308168 A308169 A308170

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved