Diagonal sums of Losanitsch's triangle (A088518?)

[Alonso Del Arte]

As you all probably already know, the diagonal sums of Pascal's
triangle are the Fibonacci numbers.

What about the diagonal sums of Losanitsch's triangle (A034851)? I
added up about a dozen diagonals and came up with 1, 1, 2, 2, 4, 5, 9,
12, 21, 29, 50. An OEIS search for this brings up one result, A088518,
Symmetric secondary structures of RNA molecules with n nucleotides.
One of the formulas given involves Fibonacci numbers, Catalan numbers
and flooring n/2.

Can someone verify if indeed the diagonal sums of Losanitsch's
triangle give this biochemically related sequence?

Alonso