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A241315     Number of partitions p of n into distinct parts, not including ceiling(mean(p)). 6
0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 7, 7, 10, 12, 15, 17, 23, 26, 32, 38, 45, 53, 65, 73, 87, 101, 120, 138, 160, 184, 211, 249, 285, 324, 373, 419, 487, 561, 633, 715, 808, 922, 1040, 1188, 1336, 1500, 1695, 1897, 2119, 2405, 2704, 3032, 3383, 3761, 4185, 4691 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..55.

FORMULA

a(n) + A241314(n) = A000009(n) for n >= 1.

EXAMPLE

a(10) counts these 7 partitions:  91, 82, 73, 721, 64, 631, 532.

MATHEMATICA

z = 30; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];

    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241312 *)

    Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241313 *)

    Table[Count[f[n], p_ /; MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241314 *)

    Table[Count[f[n], p_ /; ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241315 *)

    Table[Count[f[n], p_ /; MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241316 *)

    Table[Count[f[n], p_ /; ! MemberQ[p, Round[Mean[p]]]], {n, 0, ] (* A241317 *)

CROSSREFS

Cf. A241312, A241313, A241314, A241318, A000009.

Sequence in context: A244903 A167932 A006087 * A136330 A294267 A301763

Adjacent sequences:  A241312 A241313 A241314 * A241316 A241317 A241318

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 19 2014

STATUS

approved

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Last modified April 5 13:14 EDT 2020. Contains 333241 sequences. (Running on oeis4.)