Refining the Stern Diatomic Sequence
نویسندگان
چکیده
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, k) as well as for various of their associated generating functions. Relationships with Lucas polynomials and other number theoretic functions are discussed.
منابع مشابه
NON-CONVERGING CONTINUED FRACTIONS RELATED TO THE STERN DIATOMIC SEQUENCE by
— This note is essentially an addendum to the recent article of Dilcher and Stolarsky [7] though some results presented here may be of independent interest. We prove the transcendence of some irregular continued fractions which are related to the Stern diatomic sequence. The proofs of our results rest on the so-called Mahler method.
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