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A241335
Number of partitions p of n not including floor(mean(p)) as a part.
6
1, 0, 0, 0, 1, 1, 3, 4, 7, 9, 15, 18, 29, 36, 49, 65, 91, 108, 152, 184, 244, 311, 394, 473, 639, 772, 955, 1182, 1495, 1772, 2273, 2698, 3337, 4064, 4873, 5832, 7391, 8667, 10277, 12334, 15177, 17698, 21530, 25073, 30033, 36151, 42230, 48931, 59869, 69475
OFFSET
0,7
EXAMPLE
a(6) counts these 3 partitions: 51, 42, 411.
MATHEMATICA
z = 30; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241334 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241335 *)
Table[Count[f[n], p_ /; MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241336 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241337 *)
Table[Count[f[n], p_ /; MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241338 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241339 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 20 2014
STATUS
approved