OFFSET
1,4
COMMENTS
Essentially the same as A002865, but here a(1) = 1 not 0.
Also number of regions in the last section of the set of partitions of n.
Also number of partitions of n+k that are formed by k+1 sections, k >= 0 (Cf. A194799). - Omar E. Pol, Jan 30 2012
For the definition of region see A206437. - Omar E. Pol, Aug 13 2013
Partial sums give A000041, n >= 1. - Omar E. Pol, Sep 04 2013
Also the number of partitions of n with no parts greater than the number of ones. - Spencer Miller, Jan 28 2023
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)
Omar E. Pol, Illustration of the seven regions of 5
FORMULA
a(n) = A083751(n) + 1. - Omar E. Pol, Mar 04 2012
a(n) = A002865(n), if n >= 2. - Omar E. Pol, Aug 13 2013
EXAMPLE
From Omar E. Pol, Aug 13 2013: (Start)
Illustration of initial terms as number of regions:
. _ _ _ _ _ _
. |_ _ _ |
. |_ _ _|_ |
. |_ _ | |
. _ _ _ _ _ |_ _|_ _|_ |
. |_ _ _ | | |
. _ _ _ _ |_ _ _|_ | | |
. |_ _ | | | | |
. _ _ _ |_ _|_ | | | | |
. _ _ |_ _ | | | | | | |
. _ |_ | | | | | | | | |
. |_| |_| |_| |_| |_| |_|
.
. 1 1 1 2 2 4
.
(End)
MATHEMATICA
Join[{1}, Drop[CoefficientList[Series[1 / Product[(1 - x^k)^1, {k, 2, 50}], {x, 0, 50}], x], 2]] (* Vincenzo Librandi, Feb 15 2018 *)
A187219[nmax_]:=Join[{1}, Differences[PartitionsP[Range[nmax]]]];
A187219[100] (* Paolo Xausa, Feb 17 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Dec 09 2011
EXTENSIONS
Better definition from Omar E. Pol, Sep 04 2013
STATUS
approved