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 A241644 Number of partitions p of n such that (number of even numbers in p) >= 2*(number of odd numbers in p). 5

%I

%S 1,0,1,0,2,0,3,1,6,4,10,11,20,23,32,44,56,76,86,124,136,193,199,293,

%T 297,430,422,619,609,884,855,1246,1217,1742,1708,2438,2423,3393,3415,

%U 4717,4845,6558,6828,9097,9653,12585,13549,17379,18987,23897,26420,32712

%N Number of partitions p of n such that (number of even numbers in p) >= 2*(number of odd numbers in p).

%C Each number in p is counted once, regardless of its multiplicity.

%F a(n) = A241643(n) + A241645(n) for n >= 0.

%F a(n) + A241641(n) = A000041(n) for n >= 0.

%e a(6) counts these 3 partitions: 6, 42, 222.

%t z = 30; f[n_] := f[n] = IntegerPartitions[n]; s0[p_] := Count[Mod[DeleteDuplicates[p], 2], 0]; s1[p_] := Count[Mod[DeleteDuplicates[p], 2], 1];

%t Table[Count[f[n], p_ /; s0[p] < 2 s1[p]], {n, 0, z}] (* A241641 *)

%t Table[Count[f[n], p_ /; s0[p] <= 2 s1[p]], {n, 0, z}] (* A241642 *)

%t Table[Count[f[n], p_ /; s0[p] == 2 s1[p]], {n, 0, z}] (* A241643 *)

%t Table[Count[f[n], p_ /; s0[p] >= 2 s1[p]], {n, 0, z}] (* A241644 *)

%t Table[Count[f[n], p_ /; s0[p] > 2 s1[p]], {n, 0, z}] (* A241645 *)

%Y Cf. A241641, A241642, A241643, A241645.

%K nonn,easy

%O 0,5

%A _Clark Kimberling_, Apr 27 2014

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Last modified May 22 10:56 EDT 2022. Contains 353949 sequences. (Running on oeis4.)