A183009 a(n) = 24*n*p(n) = 24*n*A000041(n).

24, 96, 216, 480, 840, 1584, 2520, 4224, 6480, 10080, 14784, 22176, 31512, 45360, 63360, 88704, 121176, 166320, 223440, 300960, 399168, 529056, 692760, 907200, 1174800, 1520064, 1950480, 2498496, 3177240, 4034880, 5090448, 6412032

Offset

1,1

Comments

a(n) is also the sum of the partition number of n and the "trace" Tr(n) of A183011. a(n) = p(n) + Tr(n).

a(n) is also the number of "sectors" or "half-periods" in all partitions of n in some versions of the shell model of partitions of A135010.

Links

Table of n, a(n) for n=1..32.

Formula

a(n) = A008606(n)*A000041(n) = 24*A066186(n) = n*A183008(n).

a(n) = p(n) + Tr(n) = A000041(n) + A183011(n).

a(n) = 12*M_2(n) = 24*spt(n) + 12*N_2(n) = 12*A220909(n) = 24*A092269(n) + 12*A220908(n). - Omar E. Pol, Feb 17 2013

Example

The number of partitions of 6 is p(6) = A000041(6) = 11, so a(6) = 24*6*11 = 1584.
Also the trace Tr(6) = A183011(6) = 1573, so a(6) = p(6) + Tr(6) = 11 + 1573 = 1584.

Mathematica

Table[24n*PartitionsP[n], {n, 40}] (* Harvey P. Dale, Mar 07 2019 *)

Crossrefs

Partial sums of A183006. Column 24 of A182728.

Cf. A000041, A000796, A008606, A018253, A066186, A135010, A182742, A182743, A183008, A183010, A183011.

Sequence in context: A335144 A209432 A195824 * A272871 A319577 A379773

Adjacent sequences: A183006 A183007 A183008 * A183010 A183011 A183012

Keyword

nonn,easy

Author

Omar E. Pol, Jan 22 2011

Status

approved