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 A308066 Number of triangles with perimeter n whose side lengths are even. 0
 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 3, 0, 2, 0, 4, 0, 3, 0, 5, 0, 4, 0, 7, 0, 5, 0, 8, 0, 7, 0, 10, 0, 8, 0, 12, 0, 10, 0, 14, 0, 12, 0, 16, 0, 14, 0, 19, 0, 16, 0, 21, 0, 19, 0, 24, 0, 21, 0, 27, 0, 24, 0, 30, 0, 27, 0, 33, 0, 30, 0, 37, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,14 LINKS Table of n, a(n) for n=1..79. 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))) * ((i-1) mod 2) * ((k-1) mod 2) * ((n-i-k-1) mod 2). Conjectures from Colin Barker, May 11 2019: (Start) G.f.: x^6 / ((1 - x)^3*(1 + x)^3*(1 - x + x^2)*(1 + x^2)^2*(1 + x + x^2)*(1 + x^4)). a(n) = a(n-4) + a(n-6) + a(n-8) - a(n-10) - a(n-12) - a(n-14) + a(n-18) for n>18. (End) MATHEMATICA Table[Sum[Sum[Mod[i - 1, 2] Mod[k - 1, 2] 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 Cf. A308065. Sequence in context: A108044 A104477 A224928 * A052173 A177825 A175790 Adjacent sequences: A308063 A308064 A308065 * A308067 A308068 A308069 KEYWORD nonn AUTHOR Wesley Ivan Hurt, May 10 2019 STATUS approved

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Last modified July 19 20:58 EDT 2024. Contains 374436 sequences. (Running on oeis4.)