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A241320
Number of partitions p of n into distinct parts, including floor(mean(p)) but not ceiling(mean(p)).
5
0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 4, 4, 2, 4, 8, 5, 12, 5, 10, 19, 22, 8, 21, 34, 34, 29, 54, 21, 72, 57, 83, 109, 70, 59, 158, 179, 195, 99, 259, 160, 332, 317, 270, 471, 537, 286, 542, 537, 816, 852, 1051, 751, 995, 828, 1584, 1789, 2005, 941, 2431
OFFSET
0,11
EXAMPLE
a(11) counts these 2 partitions: 641, 542.
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 19 2014
STATUS
approved