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A241322 Number of partitions p of n into distinct parts, including floor(mean(p)) or ceiling(mean(p)). 5
0, 1, 1, 2, 1, 2, 2, 3, 3, 4, 5, 7, 5, 10, 11, 12, 13, 20, 19, 28, 24, 33, 43, 53, 43, 62, 79, 88, 91, 126, 106, 163, 162, 207, 248, 236, 240, 357, 410, 462, 404, 597, 546, 754, 797, 818, 1080, 1230, 1077, 1401, 1491, 1881, 2051, 2410, 2284, 2682, 2701, 3609 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..57.

FORMULA

a(n) + A241321(n) = A000009(n) for n >= 1.

EXAMPLE

a(11) counts these 7 partitions:  {11}, {7,3,1}, {6,5}, {6,4,1}, {6,3,2}, {5,4,2}, {5,3,2,1}.

MATHEMATICA

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

    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241318 *)

    Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241319 *)

    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241320 *)

    Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241321 *)

    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] || MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241322 *)

CROSSREFS

Cf. A241318, A241319, A241320, A241321, A241312, A000009.

Sequence in context: A214130 A029172 A240864 * A275380 A161052 A161256

Adjacent sequences:  A241319 A241320 A241321 * A241323 A241324 A241325

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 19 2014

STATUS

approved

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Last modified August 6 00:46 EDT 2021. Contains 346493 sequences. (Running on oeis4.)