Help needed with new sequences

[wouter meeussen]

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.

If the triangular number is allowed to be zero, then
this reduces to {1, 2, 5, 8, 23}

If we only require one of the squares to be non-zero,
then {1} is the only non-expressible integer.

Wouter.