OFFSET
1,5
LINKS
Robert Israel, Table of n, a(n) for n = 1..1000
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))) * mu(i)^2 * mu(k)^2 * mu(n-i-k)^2 * i, where mu is the Möbius function (A008683).
MAPLE
f:= proc(n)
local a, b, t;
t:= 0;
for a from 1 to n/3 do
if not a::squarefree then next fi;
for b from max(a, ceil((n+1)/2-a)) to (n-a)/2 do
if b::squarefree and (n-a-b)::squarefree then t:= t+b fi
od od;
t
end proc:
map(f, [$1..100]); # Robert Israel, May 09 2024
MATHEMATICA
Table[Sum[Sum[i* MoebiusMu[i]^2*MoebiusMu[k]^2*MoebiusMu[n - k - i]^2 *Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 14 2019
STATUS
approved