A309394 - OEIS

%I #19 Jun 16 2020 14:37:27

%S 3,9,12,19,22,27,33,34,36,41,48,51,54,57,59,66,73,75,76,77,81,86,88,

%T 97,99,101,102,107,108,110,114,121,123,129,132,134,136,137,138,144,

%U 147,149,153,162,163,164,166,170,171,177,178,179,181,187,192,194,198

%N Perimeters of integer-sided triangles whose side lengths are square numbers.

%H Robert Israel, <a href="/A309394/b309394.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>

%p N:= 1000: # to get all terms <= N

%p S:= {}:

%p for a from 1 to floor(sqrt(N/3)) do

%p    for b from a to floor(sqrt((N-a^2)/2)) do

%p      S:= S union map(c -> a^2 + b^2 + c^2, {$b .. floor(sqrt(min(a^2+b^2-1, N-a^2-b^2)))})

%p od od:

%p sort(convert(S,list)); # _Robert Israel_, Jan 01 2020

%t Flatten[Table[If[Sum[Sum[(Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]) (Floor[Sqrt[k]] - Floor[Sqrt[k - 1]]) (Floor[Sqrt[n - k - i]] - Floor[Sqrt[n - k - i - 1]])*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}] > 0, n, {}], {n, 200}]]

%Y Cf. A308064.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Jul 28 2019