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A237831 Number of partitions of n such that (greatest part) - (least part) <= number of parts. 5
1, 2, 3, 5, 6, 10, 12, 18, 23, 32, 40, 57, 70, 94, 120, 157, 196, 256, 318, 408, 508, 640, 792, 996, 1223, 1518, 1863, 2296, 2798, 3432, 4162, 5070, 6130, 7422, 8936, 10777, 12916, 15500, 18522, 22136, 26348, 31376, 37222, 44160, 52236, 61756, 72824, 85847 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..93

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

FORMULA

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

EXAMPLE

a(6) = 10 counts all the 11 partitions of 6 except 4+1+2.

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, A237832, A237833, A237834.

Sequence in context: A105420 A058641 A212253 * A329235 A241829 A250179

Adjacent sequences:  A237828 A237829 A237830 * A237832 A237833 A237834

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 16 2014

STATUS

approved

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Last modified November 29 23:37 EST 2020. Contains 338780 sequences. (Running on oeis4.)