login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A237832 Number of partitions of n such that (greatest part) - (least part) = number of parts. 12
0, 0, 0, 1, 0, 2, 1, 3, 3, 5, 4, 10, 8, 13, 15, 22, 22, 34, 36, 51, 58, 75, 85, 116, 130, 165, 194, 244, 281, 355, 409, 505, 591, 718, 839, 1022, 1186, 1425, 1668, 1994, 2319, 2765, 3213, 3805, 4429, 5214, 6052, 7119, 8243, 9645, 11169, 13026, 15046, 17511 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..96

George E. Andrews, 4-Shadows in q-Series and the Kimberling Index, Preprint, May 15, 2016.

FORMULA

A237830(n) + a(n) + A237833(n) = A000041(n). - R. J. Mathar, Nov 24 2017

EXAMPLE

a(6) = 2 counts these partitions:  4+2, 4+1+1.

MATHEMATICA

z = 60; q[n_] := q[n] = IntegerPartitions[n]; t[p_] := t[p] = Length[p];

Table[Count[q[n], p_ /; Max[p] - Min[p] < t[p]], {n, z}]  (* A237830 *)

Table[Count[q[n], p_ /; Max[p] - Min[p] <= t[p]], {n, z}] (* A237831 *)

Table[Count[q[n], p_ /; Max[p] - Min[p] == t[p]], {n, z}] (* A237832 *)

Table[Count[q[n], p_ /; Max[p] - Min[p] > t[p]], {n, z}]  (* A237833 *)

Table[Count[q[n], p_ /; Max[p] - Min[p] >= t[p]], {n, z}] (* A237834 *)

CROSSREFS

Cf. A237830, A237831, A237833, A237834.

Sequence in context: A026927 A240863 A288005 * A074500 A107237 A070047

Adjacent sequences:  A237829 A237830 A237831 * A237833 A237834 A237835

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 16 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 24 07:04 EDT 2020. Contains 337975 sequences. (Running on oeis4.)