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A237832 Number of partitions of n such that (greatest part) - (least part) = number of parts. 5
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

REFERENCES

George E. Andrews, 4-Shadows in q-Series and the Kimberling Index, Preprint, May 15, 2016; http://www.personal.psu.edu/gea1/pdf/315.pdf

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

a(6) = 2 counts these partitions:  42, 411.

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: A178133 A026927 A240863 * A074500 A107237 A070047

Adjacent sequences:  A237829 A237830 A237831 * A237833 A237834 A237835

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 16 2014

STATUS

approved

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Last modified August 24 04:54 EDT 2017. Contains 291052 sequences.