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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 ).

See also Number Triangle
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References Losanitsch, S. M. "Die Isometrie-Arten bei den Homologen der Paraffin-Reihe." Chem. Ber. 30 , 1917-1926, 1897. Sloane,
N. J. A. http://www.research.att.com/~njas/sequences/classic.html#LOSS . Sloane,
N. J. A. Sequences A005418 and A034851 in "The On-Line Encyclopedia of Integer
Sequences." Referenced on Wolfram|Alpha Losanitsch's Triangle
Cite this as:
Weisstein, Eric W. "Losanitsch's Triangle."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/LosanitschsTriangle.html

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