A308166 Number of integer-sided triangles with perimeter n such that the smallest side divides the largest.

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

Offset

1,9

Links

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

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

Mathematica

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

Crossrefs

Cf. A307828.

Sequence in context: A359577 A030401 A275888 * A295931 A295920 A176187

Adjacent sequences: A308163 A308164 A308165 * A308167 A308168 A308169

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved