A240862 - OEIS

A240862

Number of partitions of n into distinct parts of which the number of even parts is a part.

0, 0, 0, 1, 0, 1, 2, 2, 3, 3, 5, 5, 7, 7, 10, 12, 14, 16, 19, 23, 27, 33, 37, 45, 51, 60, 68, 82, 94, 108, 123, 143, 165, 188, 214, 246, 282, 318, 362, 412, 469, 527, 597, 675, 764, 858, 965, 1086, 1223, 1367, 1530, 1717, 1923, 2144, 2393, 2674, 2981, 3315

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OFFSET

0,7

LINKS

Table of n, a(n) for n=0..57.

FORMULA

a(n) + A240869(n) = A000009(n) for n >= 0.

EXAMPLE

a(10) counts these 5 partitions: 82, 721, 631, 541, 4321.

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. A240863, A240864, A240865, A240866, A240867, A240868; for analogous sequences for unrestricted partitions, see A240573-A240579.

Sequence in context: A008667 A367221 A239880 * A177716 A109763 A321523

Adjacent sequences: A240859 A240860 A240861 * A240863 A240864 A240865

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 14 2014

STATUS

approved