A308214 Sum of the smallest side lengths of all integer-sided obtuse triangles with perimeter n.

0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 5, 0, 5, 7, 9, 7, 9, 12, 19, 12, 29, 18, 35, 25, 42, 38, 49, 46, 57, 54, 82, 68, 98, 77, 117, 97, 127, 127, 148, 138, 171, 169, 211, 181, 246, 206, 271, 246, 298, 285, 334, 325, 378, 354, 437, 385, 481, 423, 529, 489, 574, 565

Offset

1,7

Links

Table of n, a(n) for n=1..62.

Wikipedia, Integer Triangle

Formula

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

Mathematica

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

Crossrefs

Cf. A308157.

Sequence in context: A079200 A011420 A035686 * A327371 A037228 A002117

Adjacent sequences: A308211 A308212 A308213 * A308215 A308216 A308217

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved