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A241343
Number of partitions p of n such that neither floor(mean(p)) nor ceiling(mean(p)) is a part.
5
1, 0, 0, 0, 1, 1, 3, 3, 6, 8, 11, 12, 27, 23, 33, 51, 68, 67, 114, 111, 186, 217, 242, 277, 502, 501, 571, 760, 1014, 1021, 1649, 1549, 2195, 2506, 2777, 3712, 5275, 4919, 5800, 7259, 10389, 9858, 13987, 13846, 18261, 23029, 23314, 26523, 40250, 39613, 49286
OFFSET
0,7
EXAMPLE
a(6) counts these 3 partitions: 51, 42, 411.
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 20 2014
STATUS
approved