A309394 Perimeters of integer-sided triangles whose side lengths are square numbers.

3, 9, 12, 19, 22, 27, 33, 34, 36, 41, 48, 51, 54, 57, 59, 66, 73, 75, 76, 77, 81, 86, 88, 97, 99, 101, 102, 107, 108, 110, 114, 121, 123, 129, 132, 134, 136, 137, 138, 144, 147, 149, 153, 162, 163, 164, 166, 170, 171, 177, 178, 179, 181, 187, 192, 194, 198

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Wikipedia, Integer Triangle

Maple

N:= 1000: # to get all terms <= N
S:= {}:
for a from 1 to floor(sqrt(N/3)) do
   for b from a to floor(sqrt((N-a^2)/2)) do
     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)))})
od od:
sort(convert(S, list)); # Robert Israel, Jan 01 2020

Mathematica

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}]]

Crossrefs

Cf. A308064.

Sequence in context: A261953 A297001 A356220 * A285564 A140979 A096726

Adjacent sequences: A309391 A309392 A309393 * A309395 A309396 A309397

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 28 2019

Status

approved