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A241340 Number of partitions p of n such that floor(mean(p)) and ceiling(mean(p)) are parts of p. 5
0, 1, 2, 3, 4, 5, 7, 8, 11, 15, 18, 22, 37, 36, 50, 73, 89, 100, 152, 161, 249, 290, 330, 413, 646, 666, 803, 1060, 1348, 1473, 2170, 2183, 3003, 3455, 3984, 5318, 6936, 6839, 8494, 10664, 14064, 14322, 19343, 20418, 26417, 32021, 34068, 40921, 56205, 57543 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..49.

FORMULA

a(n) + A241344(n) = A000041(n) for n >=1.

EXAMPLE

a(6) counts these 8 partitions:  6, 33, 321, 3111, 222, 2211, 21111, 111111.

MATHEMATICA

z = 30; f[n_] := f[n] = IntegerPartitions[n];

    t1 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241340 *)

    t2 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241341 *)

    t3 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241342 *)

    t4 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241343 *)

    t5 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] || MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241344 *)

CROSSREFS

Cf. A241341, A241342, A241343, A241344.

Sequence in context: A309879 A191166 A238484 * A326667 A293441 A306203

Adjacent sequences:  A241337 A241338 A241339 * A241341 A241342 A241343

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 20 2014

STATUS

approved

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Last modified June 5 09:20 EDT 2020. Contains 334829 sequences. (Running on oeis4.)