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Losanitsch's triangle (OEIS A034851) is a number triangle for which each term is the sum of
the two numbers immediately above it, except that, numbering the rows by 
, 1, 2, ... and the entries in each row by 
, 1, 2, ..., 
, are given by the recurrence equations
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where 
is a binomial coefficient.
can be written in closed form as
![a(n,k)=1/2[(n; k)+(n (mod 2); k (mod 2))(|_1/2n_|; |_1/2k_|)].](/images/equations/LosanitschsTriangle/NumberedEquation3.svg) |
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The plot above shows the binary representations for the first 255 (top figure) and 511 (bottom figure) terms of a flattened Losanitsch's triangle.
The row sums of Losanitsch's triangle are
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the first few terms of which are 1, 2, 3, 6, 10, 20, 36, ... (OEIS A005418).
