A308108 Sum of the largest side lengths of all integer-sided scalene triangles with perimeter n.

0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 5, 5, 12, 6, 20, 14, 31, 23, 43, 35, 66, 48, 83, 73, 113, 91, 145, 123, 183, 157, 223, 197, 281, 239, 330, 300, 399, 351, 471, 423, 552, 498, 636, 582, 745, 669, 842, 782, 966, 882, 1094, 1010, 1234, 1142, 1378, 1286, 1554, 1434

Offset

1,9

Links

Table of n, a(n) for n=1..58.

Wikipedia, Integer Triangle

Formula

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

Conjectures from Colin Barker, May 13 2019: (Start)

G.f.: x^9*(2 + x + x^2)^2 / ((1 - x)^4*(1 + x)^3*(1 + x^2)^2*(1 + x + x^2)^2).

a(n) = -a(n-1) + 2*a(n-3) + 4*a(n-4) + 2*a(n-5) - a(n-6) - 5*a(n-7) - 5*a(n-8) - a(n-9) + 2*a(n-10) + 4*a(n-11) + 2*a(n-12) - a(n-14) - a(n-15) for n>15.

(End)

Mathematica

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

Crossrefs

Cf. A307966.

Sequence in context: A016578 A268631 A335775 * A320374 A264757 A195773

Adjacent sequences: A308105 A308106 A308107 * A308109 A308110 A308111

Keyword

nonn

Author

Wesley Ivan Hurt, May 13 2019

Status

approved