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A240575 Number of partitions of n such that the number of even parts is a part and the number of odd parts is a part. 7
0, 0, 0, 1, 1, 2, 2, 3, 4, 5, 8, 10, 14, 16, 25, 28, 40, 47, 65, 77, 101, 122, 158, 193, 239, 295, 363, 449, 539, 670, 800, 989, 1169, 1439, 1701, 2083, 2442, 2975, 3493, 4224, 4941, 5944, 6955, 8313, 9706, 11538, 13475, 15936, 18568, 21859, 25466, 29847 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..51.

EXAMPLE

a(10) counts these 8 partitions:  721, 6211, 5221, 4321, 43111, 421111, 3322, 32221.

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

Cf. A240573, A240574, A240576, A240577, A240578, A240579.

Sequence in context: A186505 A228693 A116676 * A176538 A285261 A100483

Adjacent sequences:  A240572 A240573 A240574 * A240576 A240577 A240578

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 10 2014

STATUS

approved

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Last modified January 25 08:59 EST 2022. Contains 350565 sequences. (Running on oeis4.)