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 A308068 Number of integer-sided triangles with perimeter n whose longest side length is even. 0
 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 1, 1, 3, 3, 2, 2, 5, 5, 3, 3, 7, 7, 5, 5, 9, 9, 7, 7, 12, 12, 9, 9, 15, 15, 12, 12, 18, 18, 15, 15, 22, 22, 18, 18, 26, 26, 22, 22, 30, 30, 26, 26, 35, 35, 30, 30, 40, 40, 35, 35, 45, 45, 40, 40, 51, 51, 45, 45, 57, 57, 51, 51 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 LINKS Table of n, a(n) for n=1..72. Wikipedia, Integer Triangle FORMULA a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * ((n-i-k-1) mod 2). Conjectures from Colin Barker, May 11 2019: (Start) G.f.: x^5 / ((1 - x)^3*(1 + x)^2*(1 - x + x^2)*(1 + x^2)^2*(1 + x + x^2)). a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-4) - a(n-5) + 2*a(n-6) - 2*a(n-7) + a(n-8) - a(n-9) - a(n-10) + a(n-11) - a(n-12) + a(n-13) for n>13. (End) MATHEMATICA Table[Sum[Sum[Mod[n - i - k - 1, 2]*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}] CROSSREFS Sequence in context: A295515 A348890 A110659 * A100522 A258140 A140408 Adjacent sequences: A308065 A308066 A308067 * A308069 A308070 A308071 KEYWORD nonn AUTHOR Wesley Ivan Hurt, May 10 2019 STATUS approved

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Last modified August 11 08:53 EDT 2024. Contains 375059 sequences. (Running on oeis4.)