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Congruences Modulo Small Powers of 2 and 3 for Partitions into Odd Designated Summands
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B. Hemanthkumar

Department of Mathematics

M. S. Ramaiah University of Applied Sciences

Bengaluru-560 058

India

H. S. Sumanth Bharadwaj and M. S. Mahadeva Naika

Department of Mathematics

Central College Campus

Bangalore University

Bengaluru-560 001

India

**Abstract:**

Andrews, Lewis and Lovejoy introduced a new class of partitions,
partitions with designated summands. Let PD(*n*) denote the number of
partitions of *n* with designated summands and PDO(*n*) denote the number
of partitions of *n* with designated summands in which all parts are odd.
Andrews et al. established many congruences modulo 3 for PDO(*n*) by
using the theory of modular forms. Baruah and Ojah obtained numerous
congruences modulo 3, 4, 8 and 16 for PDO(*n*) by using theta function
identities. In this paper, we prove several infinite families of
congruences modulo 9, 16 and 32 for PDO(*n*).

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(Concerned with sequences
A077285
A102186.)

Received October 25 2016; revised version received January 13 2017; January 23 2017.
Published in *Journal of Integer Sequences*, January 28 2017.

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