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A240864     Number of partitions of n into distinct parts of which the number of even parts and the number of odd parts are parts. 7
0, 0, 0, 1, 0, 1, 1, 2, 1, 2, 2, 3, 3, 4, 5, 6, 8, 8, 11, 10, 17, 15, 23, 19, 32, 26, 42, 35, 57, 49, 73, 66, 95, 90, 119, 121, 153, 161, 191, 214, 239, 280, 298, 365, 373, 470, 462, 603, 576, 763, 714, 963, 889, 1205, 1102, 1502, 1371, 1857, 1696, 2289 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..59.

EXAMPLE

a(15) counts these 6 partitions:  {14,1}, {12,2,1}, {9,3,2,1}, {7,4,3,1}, {6,5,3,1}, {5,4,3,2,1}.

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, A240865, A240866, A240867, A204868; for analogous sequences for unrestricted partitions, see A240573-A240579.

Sequence in context: A161228 A214130 A029172 * A241322 A275380 A161052

Adjacent sequences:  A240861 A240862 A240863 * A240865 A240866 A240867

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 14 2014

STATUS

approved

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Last modified August 4 05:02 EDT 2021. Contains 346442 sequences. (Running on oeis4.)