|
%I #13 Jun 18 2020 13:36:09
%S 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,
%T 15,12,12,18,18,15,15,22,22,18,18,26,26,22,22,30,30,26,26,35,35,30,30,
%U 40,40,35,35,45,45,40,40,51,51,45,45,57,57,51,51
%N Number of integer-sided triangles with perimeter n whose longest side length is even.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>
%F 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).
%F Conjectures from _Colin Barker_, May 11 2019: (Start)
%F G.f.: x^5 / ((1 - x)^3*(1 + x)^2*(1 - x + x^2)*(1 + x^2)^2*(1 + x + x^2)).
%F 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.
%F (End)
%t 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}]
%K nonn
%O 1,9
%A _Wesley Ivan Hurt_, May 10 2019
|
