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A240578
Number of partitions of n such that the number of odd parts is a part and the number of even parts is not a part.
7
0, 1, 0, 0, 0, 1, 0, 2, 2, 6, 3, 8, 9, 18, 15, 27, 33, 48, 55, 73, 101, 122, 162, 183, 272, 293, 421, 436, 666, 670, 1002, 989, 1522, 1483, 2237, 2152, 3303, 3155, 4762, 4521, 6874, 6498, 9754, 9188, 13825, 12995, 19345, 18139, 27013, 25297, 37332, 34909
OFFSET
0,8
EXAMPLE
a(9) counts these 6 partitions: 531, 51111, 441, 4221, 333, 22221.
MATHEMATICA
z = 62; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}] (* A240573 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240574 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240575 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] || MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240576 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240577 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240578 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240579 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 10 2014
STATUS
approved