Help needed with new sequences

[hv at crypt.org]

"wouter meeussen" <wouter.meeussen at pandora.be> wrote:
:it seems {1, 2, 3, 5, 8, 11, 23} are the only integers
:that cannot be expressed as the sum of two squares and
:a triangular number, all three strictly positive.

Hmm:
3 = 1^2 + 1^2 + T(1)
5 = 1^2 + 1^2 + T(2)
8 = 1^2 + 1^2 + T(3)
11 = 1^2 + 3^2 + T(1)
   = 2^2 + 2^2 + T(2)
   = 2^2 + 1^2 + T(3)
23 = 2^2 + 4^2 + T(2)
   = 1^2 + 4^2 + T(3)
   = 2^2 + 3^2 + T(4)
   = 2^2 + 2^2 + T(5)
   = 1^2 + 1^2 + T(6)

Am I misunderstanding the question?

Hugo