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A240576
Number of partitions of n such that the number of even parts is a part or the number of odd parts is a part.
7
0, 1, 0, 1, 2, 4, 5, 9, 12, 21, 24, 36, 47, 69, 82, 116, 149, 197, 247, 318, 411, 515, 656, 800, 1042, 1249, 1602, 1893, 2456, 2860, 3677, 4246, 5474, 6271, 8021, 9120, 11683, 13208, 16794, 18899, 24018, 26898, 33990, 37928, 47843, 53203, 66788, 74026, 92757
OFFSET
0,5
EXAMPLE
a(6) counts these 5 partitions: 42, 411, 321, 2211, 21111.
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