

A241321


Number of partitions p of n into distinct parts, including neither floor(mean(p)) nor ceiling(mean(p)).


5



0, 0, 0, 0, 1, 1, 2, 2, 3, 4, 5, 5, 10, 8, 11, 15, 19, 18, 27, 26, 40, 43, 46, 51, 79, 80, 86, 104, 131, 130, 190, 177, 228, 241, 264, 349, 428, 403, 454, 520, 709, 663, 880, 856, 1019, 1230, 1224, 1360, 1833, 1863, 2167, 2216, 2531, 2710, 3434, 3696, 4407
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OFFSET

0,7


LINKS

Table of n, a(n) for n=0..56.


FORMULA

a(n) + A241322(n) = A000009(n) for n >= 1.


EXAMPLE

a(11) counts these 5 partitions: {10,1}, {9,2}, {8,3}, {8,2,1}, {7,4}.


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, A241322, A241312, A000009.
Sequence in context: A332285 A324325 A318284 * A093936 A329904 A331307
Adjacent sequences: A241318 A241319 A241320 * A241322 A241323 A241324


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Apr 19 2014


STATUS

approved



