login
A241315
Number of partitions p of n into distinct parts, not including ceiling(mean(p)).
6
0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 7, 7, 10, 12, 15, 17, 23, 26, 32, 38, 45, 53, 65, 73, 87, 101, 120, 138, 160, 184, 211, 249, 285, 324, 373, 419, 487, 561, 633, 715, 808, 922, 1040, 1188, 1336, 1500, 1695, 1897, 2119, 2405, 2704, 3032, 3383, 3761, 4185, 4691
OFFSET
0,7
FORMULA
a(n) + A241314(n) = A000009(n) for n >= 1.
EXAMPLE
a(10) counts these 7 partitions: 91, 82, 73, 721, 64, 631, 532.
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