OFFSET
0,3
COMMENTS
The mentioned view of the section model looks like a tree (see example). Note that every column contains the same parts. For more information about the section model of partitions see A135010 and A194803.
Number of partitions of 2n-1 such that n-1 or n is a part, for n >=1. - Clark Kimberling, Mar 01 2014
LINKS
Robert Price, Table of n, a(n) for n = 0..5000
FORMULA
EXAMPLE
Illustration of one of the three views with seven sections:
.
. 1
. 2 1
. 1 3
. 2 1
. 4 1
. 1 3
. 1 5
. 2 1
. 4 1
. 3 1
. 6 1
. 3
. 5
. 4
. 7
.
There are 25 parts that are visible, so a(7) = 25.
Using the formula we have a(7) = p(7) + p(7-1) - 1 = 15 + 11 - 1 = 25, where p(n) is the number of partitions of n.
MATHEMATICA
Table[Count[IntegerPartitions[2 n - 1], p_ /; Or[MemberQ[p, n - 1], MemberQ[p, n]]], {n, 50}] (* Clark Kimberling, Mar 01 2014 *)
Table[PartitionsP[n] + PartitionsP[n-1] - 1, {n, 0, 44}] (* Robert Price, May 12 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jan 27 2012
STATUS
approved