Diagonal sums of Losanitsch's triangle (A088518?)

[Alonso Del Arte]

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

Christian Bower points out that the sequence in one piece is already
in the OEIS, A102526. Even so, it's interesting to notice that this
particular sequence from Losanitsch's triangle, like other sequences
in the triangle, interweave two sequences. Thank you for this insight.

Al

> 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
> >
>


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