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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 LINKS Table of n, a(n) for n=0..60. 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 Adjacent sequences: A240864 A240865 A240866 * A240868 A240869 A240870 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 14 2014 STATUS approved

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Last modified September 8 15:19 EDT 2024. Contains 375753 sequences. (Running on oeis4.)