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A307828 Number of integer-sided triangles with perimeter n such that the smallest side divides n. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

LINKS

Table of n, a(n) for n=1..80.

FORMULA

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1)) * chi(n/k), where chi is the integer characteristic.

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}]

CROSSREFS

Cf. A005044.

Sequence in context: A030272 A157128 A301376 * A280698 A217667 A240850

Adjacent sequences:  A307825 A307826 A307827 * A307829 A307830 A307831

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 15 2019

STATUS

approved

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Last modified March 29 18:36 EDT 2020. Contains 333117 sequences. (Running on oeis4.)