

A243223


Number of partitions of n into positive summands in arithmetic progression with common difference 3.


3



0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 2, 0, 1, 2, 1, 0, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 0, 3, 1, 1, 1, 1, 2, 3, 0, 1, 2, 2, 0, 3, 1, 1, 2, 1, 1, 3, 0, 2, 2, 1, 0, 3, 3, 1, 1, 1, 1, 4, 0, 2, 2, 1, 1, 3, 1, 1, 2, 2, 1, 3, 0, 1, 3, 2, 1, 3, 1, 2, 1, 1
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OFFSET

1,15


COMMENTS

This sequence gives the number of ways to write n as n = a + a+3 + ... + a+3r = (r+1)(2a+3r)/2, with a and r integers > 0.


LINKS

JeanChristophe Hervé, Table of n, a(n) for n = 1..10045
J. W. Andrushkiw, R. I. Andrushkiw and C. E. Corzatt, Representations of Positive Integers as Sums of Arithmetic Progressions, Mathematics Magazine, Vol. 49, No. 5 (Nov., 1976), pp. 245248.
M. A. Nyblom and C. Evans, On the enumeration of partitions with summands in arithmetic progression, Australasian Journal of Combinatorics, Vol. 28 (2003), pp. 149159.


FORMULA

a(n) = d1(n)  1  f(n) with d1(n) = number of odd divisors of n (A001227) and f(n) = the number of those odd divisors d of n such that d > 1 and d(1+d/3)/2 <= n <= 3d(d1)/2. f(n) is in A243224.


EXAMPLE

a(15) = 2 because 15 = 6 + 9 = 2 + 5 + 8.


CROSSREFS

Cf. A072670 (same with common differences = 2).
A243225 gives the integers n that are not such sums for which a(n) = 0.
Sequence in context: A088434 A205745 A333781 * A034178 A317531 A074169
Adjacent sequences: A243220 A243221 A243222 * A243224 A243225 A243226


KEYWORD

nonn


AUTHOR

JeanChristophe Hervé, Jun 01 2014


STATUS

approved



