

A121895


Number of partitions of n into 4 summands a>=b>=c>=d>0 with integer a/b, b/c and c/d.


1



0, 0, 0, 1, 1, 2, 2, 4, 2, 5, 4, 6, 4, 7, 5, 10, 5, 8, 6, 11, 8, 13, 6, 12, 7, 13, 9, 15, 8, 16, 10, 17, 10, 14, 10, 20, 11, 14, 10, 23, 10, 22, 12, 21, 15, 20, 8, 21, 12, 23, 18, 24, 11, 20, 15, 30, 18, 21, 8, 28, 14, 21, 18, 32, 16, 34, 16, 22, 15, 28, 14, 33, 14, 22, 20, 31, 18, 32, 15
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OFFSET

1,6


LINKS

Table of n, a(n) for n=1..79.


FORMULA

a(n) = Sum_{dn, d>1} A122935(d1).  Franklin T. AdamsWatters, Sep 20 2006


EXAMPLE

a(36)=20 because there are 20 partitions of 36 in 4 summands a>=b>=c>=d>0 with integer a/b, b/c and c/d:
{33, 1, 1, 1}, {32, 2, 1, 1}, {30, 2, 2, 2}, {28, 4, 2, 2}, {27, 3, 3, 3}, {25, 5, 5, 1}, {24, 8, 2, 2}, {24, 6, 3, 3}, {24, 4, 4, 4}, {21, 7, 7, 1}, {20, 10, 5, 1}, {18, 6, 6, 6}, {17, 17, 1, 1}, {16, 16, 2, 2}, {16, 8, 8, 4}, {15, 15, 5, 1}, {15, 15, 3, 3}, {14, 14, 7, 1}, {12, 12, 6, 6}, {9, 9, 9, 9}.


CROSSREFS

Cf. A026810 = number of partitions of n into exactly 4 parts.
Column 4 of A122934.
Cf. A049822, A003238.
Sequence in context: A233520 A243271 A232245 * A139555 A241814 A088371
Adjacent sequences: A121892 A121893 A121894 * A121896 A121897 A121898


KEYWORD

nonn


AUTHOR

Zak Seidov, Sep 01 2006


STATUS

approved



