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A241313
Number of partitions p of n into distinct parts, not including floor(mean(p)).
6
0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 7, 10, 11, 15, 16, 22, 25, 31, 35, 45, 51, 61, 70, 85, 98, 116, 131, 156, 176, 209, 238, 276, 314, 356, 411, 479, 539, 612, 688, 792, 891, 1022, 1149, 1295, 1462, 1641, 1831, 2088, 2346, 2637, 2941, 3277, 3648, 4097, 4575
OFFSET
0,7
FORMULA
a(n) + A241312(n) = A000009(n) for n >= 1.
EXAMPLE
a(10) counts these 6 partitions: 91, 82, 73, 721, 64, 631.
MATHEMATICA
z = 30;
f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241312 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241313 *)
Table[Count[f[n], p_ /; MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241314 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241315 *)
Table[Count[f[n], p_ /; MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241316 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Round[Mean[p]]]], {n, 0, ] (* A241317 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 19 2014
STATUS
approved