A243216 Sum of integer partitions of n, with each partition being read as a decimal number.

1, 13, 135, 1379, 13832, 138630, 1386735, 13870508, 138709809, 1387130199, 13871350327, 138713829423, 1387138784462, 13871391119415, 138713916151110, 1387139194337991, 13871391993095355, 138713920259792085, 1387139203095898387, 13871392034248925832

Offset

1,2

Comments

Parts greater than 9 are treated according to their decimal digits. For example, the four partitions of 12 with parts greater than 9 are: {12}, {11, 1}, {10, 2}, and {10, 1, 1}. Read as decimal numbers, they become 12, 111, 102, and 1011.

Links

Table of n, a(n) for n=1..20.

Example

The integer partitions of 5 are: {5}, {4, 1}, {3, 2}, {3, 1, 1}, {2, 2, 1}, {2, 1, 1, 1}, and {1, 1, 1, 1, 1}.  Read as decimal numbers, they are 5, 41, 32, 311, 221, 2111, and 11111, the total of which is 13832, so a(5) = 13832.

Mathematica

Table[Total[FromDigits/@IntegerPartitions[n]], {n, 25}]

Crossrefs

Sequence in context: A130774 A179619 A019519 * A112225 A069511 A052262

Adjacent sequences: A243213 A243214 A243215 * A243217 A243218 A243219

Keyword

nonn,base

Author

Harvey P. Dale, Jun 01 2014

Status

approved