A308218 Take the integer-sided obtuse triangles with perimeter n and sides a, b and c such that a <= b <= c. a(n) is the sum of all the b's.

0, 0, 0, 0, 0, 0, 2, 0, 3, 0, 7, 0, 9, 9, 15, 11, 18, 18, 32, 21, 51, 30, 64, 41, 79, 62, 95, 77, 113, 93, 151, 124, 186, 144, 221, 177, 249, 225, 289, 253, 333, 310, 411, 343, 479, 390, 534, 456, 593, 527, 674, 605, 756, 667, 859, 733, 954, 826, 1049, 936

Offset

1,7

Links

Table of n, a(n) for n=1..60.

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))) i.

Mathematica

Table[Sum[Sum[i (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. A308216.

Sequence in context: A076563 A163974 A317443 * A067165 A079981 A117776

Adjacent sequences: A308215 A308216 A308217 * A308219 A308220 A308221

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2019

Status

approved