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

1,9

Links

Antti Karttunen, Table of n, a(n) for n = 1..10220

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

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}]

Prog

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

Crossrefs

Cf. A005044.

Sequence in context: A157128 A359899 A301376 * A280698 A217667 A240850

Adjacent sequences: A307825 A307826 A307827 * A307829 A307830 A307831

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved