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A237830 Number of partitions of n such that (greatest part) - (least part) < number of parts. 5
1, 2, 3, 4, 6, 8, 11, 15, 20, 27, 36, 47, 62, 81, 105, 135, 174, 222, 282, 357, 450, 565, 707, 880, 1093, 1353, 1669, 2052, 2517, 3077, 3753, 4565, 5539, 6704, 8097, 9755, 11730, 14075, 16854, 20142, 24029, 28611, 34009, 40355, 47807, 56542, 66772, 78728 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

a(n) + A237834(n) = A000041(n). - R. J. Mathar, Nov 24 2017

EXAMPLE

a(6) = 8 counts these partitions:  6, 3+3, 4+1+1, 3+2+1, 2+2+2, 3+1+1+1, 2+2+1+1, 2+1+1+1+1, 1+1+1+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. A237831-A237834.

Sequence in context: A035990 A036001 A027336 * A023434 A087192 A188917

Adjacent sequences:  A237827 A237828 A237829 * A237831 A237832 A237833

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 16 2014

STATUS

approved

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Last modified November 25 19:43 EST 2020. Contains 338625 sequences. (Running on oeis4.)