A308159 - OEIS

%I #9 Jun 16 2020 14:28:20

%S 0,0,1,0,2,2,6,3,7,8,14,9,16,17,25,19,28,29,40,32,43,45,58,48,62,64,

%T 79,68,84,86,104,91,109,112,132,117,138,141,163,147,170,173,198,180,

%U 205,209,236,216,244,248,277,256,286,290,322,299,331,336,370,345

%N Sum of the largest sides of all integer-sided isosceles triangles with perimeter n.

%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))) * ([i=k] + [i=n-i-k] - [k=n-i-k]) * (n-i-k), where [] is the Iverson bracket.

%F Conjectures from _Colin Barker_, May 15 2019: (Start)

%F G.f.: x^3*(1 + 2*x^2 + x^3 + 4*x^4 + x^5 + x^6) / ((1 - x)^3*(1 + x)^2*(1 + x^2)^2*(1 + x + x^2)).

%F a(n) = a(n-3) + 2*a(n-4) - 2*a(n-7) - a(n-8) + a(n-11) for n>11.

%F (End)

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

%Y Cf. A308158.

%K nonn

%O 1,5

%A _Wesley Ivan Hurt_, May 14 2019