A natural probability measure derived from Stern’s diatomic sequence
نویسندگان
چکیده
منابع مشابه
Refining the Stern Diatomic Sequence
We refine the celebrated Stern Diatomic Sequence {b(n)}n≥0, in which b(n) is the number of partitions of n into powers of 2 for which each part has multiplicity 1 or 2, by studying the sequence {b(n, k)}n,k≥0, in which b(n, k) counts the partitions of n into powers of 2 in which exactly k parts have multiplicity 2, the remaining parts being of multiplicity 1. We find closed formulas for the b(n...
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Continued fractions are linked to Stern’s diatomic sequence 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, . . . (given by the recursion relations α2n = αn and α2n+1 = αn + αn+1, where α0 = 0 and α1 = 1), which has long been known. Using a particular multidimensional continued fraction algorithm (the Farey algorithm), we generalize the diatomic sequence to a sequence of numbers that quite naturally can be terme...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2018
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa170709-22-1