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A238479 Number of partitions of n whose median is not a part. 5
0, 0, 1, 1, 2, 3, 4, 5, 8, 10, 13, 18, 23, 30, 40, 50, 64, 83, 104, 131, 166, 206, 256, 320, 394, 485, 598, 730, 891, 1088, 1318, 1596, 1932, 2326, 2797, 3360, 4020, 4804, 5735, 6824, 8108, 9624, 11392, 13468, 15904, 18737, 22048, 25914, 30400, 35619, 41686 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Also, the number of partitions p of n such that (1/2)*max(p) is a part of p.

LINKS

Table of n, a(n) for n=1..51.

FORMULA

A238478(n) + A238479(n) = A000041(n).

For all n, A027187(n) >= a(n). [Because when a partition of n has an odd number of parts, then it is not counted by this sequence (cf. A238478) and also some of the partitions with an even number of parts might be excluded here. Cf. Examples.] - Antti Karttunen, Feb 27 2014

EXAMPLE

a(6) counts these partitions:  51, 42, 2211 which all have an even number of parts, and their medians 3, 3 and 1.5 are not present. Note that the partitions 33 and 3111, although having an even number of parts, are not included in the count of a(6), but instead in that of A238478(6), as their medians, 3 for the former and 1 for the latter, are present in those partitions.

MATHEMATICA

Table[Count[IntegerPartitions[n], p_ /; !MemberQ[p, Median[p]]], {n, 40}]

(* also *)

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Max[p]/2]], {n, 50}]

CROSSREFS

Cf. A027187, A238478, A238480, A238481.

Sequence in context: A325109 A080713 A058664 * A035562 A107234 A035943

Adjacent sequences:  A238476 A238477 A238478 * A238480 A238481 A238482

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 27 2014

STATUS

approved

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Last modified November 30 02:27 EST 2020. Contains 338780 sequences. (Running on oeis4.)