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A240867
Number of partitions of n into distinct parts of which the number of odd parts is a part and the number of even parts is not a part.
7
0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 3, 2, 5, 2, 7, 4, 12, 5, 16, 8, 23, 11, 32, 17, 43, 25, 56, 36, 73, 51, 93, 74, 118, 102, 150, 140, 188, 191, 236, 255, 294, 337, 369, 442, 458, 570, 574, 732, 716, 930, 894, 1174, 1113, 1467, 1389, 1830, 1727, 2259
OFFSET
0,12
EXAMPLE
a(13) counts these 3 partitions: 931, 841, 6421.
MATHEMATICA
z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
t1 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}] (* A240862 *)
t2 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240863, *)
t3 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240864 *)
t4 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] || MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240865 *)
t5 = Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240866 *)
t6 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240867 *)
t7 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240868 *)
CROSSREFS
Cf. A240862, A240863, A240864, A240865, A240866, A240868; for analogous sequences for unrestricted partitions, see A240573-A240579.
Sequence in context: A111079 A165006 A134735 * A242363 A050360 A175003
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 14 2014
STATUS
approved