Rocky Mountain Journal of Mathematics

Recurrence relation for computing a bipartition function

D.S. Gireesh and M.S. Mahadeva Naika

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Recently, Merca found the recurrence relation for computing the partition function $p(n)$ which requires only the values of $p(k)$ for $k\leq n/2$. In this article, we find the recurrence relation to compute the bipartition function $p_{-2}(n)$ which requires only the values of $p_{-2}(k)$ for $k\leq n/2$. In addition, we also find recurrences for $p(n)$ and $q(n)$ (number of partitions of $n$ into distinct parts), relations connecting $p(n)$ and $q_0(n)$ (number of partitions of $n$ into distinct odd parts).

Article information

Rocky Mountain J. Math., Volume 48, Number 1 (2018), 237-247.

First available in Project Euclid: 28 April 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05A17: Partitions of integers [See also 11P81, 11P82, 11P83] 11P81: Elementary theory of partitions [See also 05A17] 11P82: Analytic theory of partitions

Recurrence relation partition bipartition


Gireesh, D.S.; Naika, M.S. Mahadeva. Recurrence relation for computing a bipartition function. Rocky Mountain J. Math. 48 (2018), no. 1, 237--247. doi:10.1216/RMJ-2018-48-1-237.

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