Diagonal sums of Losanitsch's triangle (A088518?)

[Max A.]

Alonso,

Sequence of the diagonal sums of Losanitsch's triangle is an
interweaving of two sequences: A005207 and A051450. Look:

The diagonal sums:
1, 1, 2, 2, 4, 5, 9, 12, 21, 30, 51, 76, 127, 195, 322, 504, 826,
1309, 2135, 3410, 5545, 8900, 14445, 23256, 37701, 60813, 98514,
159094, 257608, 416325, 673933, 1089648, 1763581, 2852242, 4615823,
7466468, 12082291, 19546175, 31628466, 51170460

A005207:
1, 2, 4, 9, 21, 51, 127, 322, 826, 2135, 5545, 14445, 37701, 98514,
257608, 673933, 1763581, 4615823, 12082291, 31628466

A051450:
1, 2, 5, 12, 30, 76, 195, 504, 1309, 3410, 8900, 23256, 60813, 159094,
416325, 1089648, 2852242, 7466468, 19546175, 51170460

In particular, if D(m) denotes the m-th diagonal sum (i.e., the sum
over n+k=m) of Losanitsch's triangle, then

D(2*m) = A005207(m) = (F(2*m-1) + F(m+1)) / 2

D(2*m+1) = A051450(m) = (F(2*m) + F(m)) / 2

where F() are Fibonacci numbers.

Max

On 6/28/06, Alonso Del Arte <alonso.delarte at gmail.com> wrote:
> 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
>