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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
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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).