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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

%I #4 Apr 17 2014 14:29:53

%S 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,

%T 295,363,449,539,670,800,989,1169,1439,1701,2083,2442,2975,3493,4224,

%U 4941,5944,6955,8313,9706,11538,13475,15936,18568,21859,25466,29847

%N Number of partitions of n such that the number of even parts is a part and the number of odd parts is a part.

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

%t z = 62; f[n_] := f[n] = IntegerPartitions[n];

%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}] (* A240573 *)

%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240574 *)

%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240575 *)

%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] || MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240576 *)

%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240577 *)

%t Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240578 *)

%t Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]] && ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240579 *)

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

%K nonn,easy

%O 0,6

%A _Clark Kimberling_, Apr 10 2014

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Last modified December 3 01:24 EST 2023. Contains 367526 sequences. (Running on oeis4.)