

A236544


Number of partitions of n for which (number of occurrences of the least part) > (number of occurrences of greatest part).


3



0, 0, 0, 1, 2, 3, 7, 9, 15, 21, 32, 41, 62, 80, 109, 144, 196, 246, 331, 418, 542, 688, 882, 1097, 1397, 1739, 2176, 2690, 3352, 4108, 5082, 6206, 7603, 9255, 11277, 13632, 16540, 19931, 24023, 28826, 34618, 41361, 49461, 58900, 70117, 83238, 98766, 116804
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OFFSET

1,5


COMMENTS

The partitions of n are partitioned by the partitions counted by A236543, A236544, A236545 (see Example); consequently, A000041(n) = A236543(n) + A236544(n) + A236545(n) for n >= 1.


LINKS

Table of n, a(n) for n=1..48.


EXAMPLE

Among the 15 partitions of 7, the following 6 have #(occurrences of least part) = #(occurrences of greatest part): 7, 61, 52, 43, 421, 111111; the following 7 have " > " in place of " = ": 511, 4111, 322, 3211, 31111, 22111, 211111; and the remaining 2, have " < ": 331, 221.


MATHEMATICA

z = 65; s = Map[Map[Length, {Select[#, First[#] == Last[#] &], Select[#, First[#] > Last[#] &], Select[#, First[#] < Last[#] &]} &[Map[{Count[#, Min[#]], Count[#, Max[#]]} &, IntegerPartitions[#]]]] &, Range[z]]; t = Flatten[s];
t1 = Table[t[[3 k  2]], {k, 1, z}] (* A236543 *)
t2 = Table[t[[3 k  1]], {k, 1, z}] (* A236544 *)
t3 = Table[t[[3 k]], {k, 1, z}] (* A236545 *)
(* Peter J. C. Moses, Jan 28 2014 *)


CROSSREFS

Cf. A236543, A236545, A000041.
Sequence in context: A294122 A211539 A109660 * A075855 A140189 A327066
Adjacent sequences: A236541 A236542 A236543 * A236545 A236546 A236547


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jan 28 2014


STATUS

approved



