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A237834 Number of partitions of n such that (greatest part) - (least part) >= number of parts. 5
0, 0, 0, 1, 1, 3, 4, 7, 10, 15, 20, 30, 39, 54, 71, 96, 123, 163, 208, 270, 342, 437, 548, 695, 865, 1083, 1341, 1666, 2048, 2527, 3089, 3784, 4604, 5606, 6786, 8222, 9907, 11940, 14331, 17196, 20554, 24563, 29252, 34820, 41327, 49016, 57982, 68545, 80833 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..95

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

FORMULA

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

EXAMPLE

a(7) = 4 counts these partitions:  6+1, 5+2, 5+1+1, 4+2+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, A237832, A237833.

Sequence in context: A050572 A249668 A105343 * A147955 A147789 A047625

Adjacent sequences:  A237831 A237832 A237833 * A237835 A237836 A237837

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 16 2014

STATUS

approved

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Last modified December 2 10:24 EST 2021. Contains 349437 sequences. (Running on oeis4.)