## Rocky Mountain Journal of Mathematics

### Recurrence relation for computing a bipartition function

#### Abstract

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

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

Dates
First available in Project Euclid: 28 April 2018

https://projecteuclid.org/euclid.rmjm/1524880889

Digital Object Identifier
doi:10.1216/RMJ-2018-48-1-237

Mathematical Reviews number (MathSciNet)
MR3795741

Zentralblatt MATH identifier
1385.05020

#### Citation

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. https://projecteuclid.org/euclid.rmjm/1524880889

#### References

• B.C. Berndt, Ramanujan's notebooks, Part III, Springer-Verlag, New York, 1991.
• L. Euler, Introduction to analysis of the infinite, Springer-Verlag, New York, 1988.
• J.A. Ewell, Recurrences for the partition function and its relatives, Rocky Mountain J. Math. 34 (2004), 619–627.
• M. Merca, Fast computation of the partition function, J. Num. Th. 164 (2016), 405–416.
• S. Ramanujan, Collected papers, Cambridge University Press, Cambridge, 1927.