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A308108 Sum of the largest side lengths of all integer-sided scalene triangles with perimeter n. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,9
LINKS
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 13 2019
STATUS
approved

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Last modified May 28 01:34 EDT 2024. Contains 372900 sequences. (Running on oeis4.)