A240059 Number of partitions of n such that m(1) > m(3), where m = multiplicity.

0, 1, 1, 2, 2, 5, 6, 10, 12, 20, 25, 37, 46, 67, 84, 116, 145, 197, 246, 325, 404, 527, 653, 837, 1032, 1310, 1609, 2018, 2467, 3070, 3738, 4612, 5591, 6854, 8277, 10080, 12125, 14688, 17604, 21212, 25333, 30389, 36172, 43201, 51256, 60981, 72132, 85498

Offset

0,4

Links

Table of n, a(n) for n=0..47.

Formula

a(n) + A182714(n) + A240058(n) = A000041(n) for n >= 0.

Example

a(6) counts these 6 partitions:  51, 411, 3111, 2211, 21111, 111111.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Count[p, 1] < Count[p, 3]], {n, 0, z}]  (* A182714 *)
t2 = Table[Count[f[n], p_ /; Count[p, 1] <= Count[p, 3]], {n, 0, z}] (* A182714(n+3) *)
t3 = Table[Count[f[n], p_ /; Count[p, 1] == Count[p, 3]], {n, 0, z}] (* A240058 *)
t4 = Table[Count[f[n], p_ /; Count[p, 1] > Count[p, 3]], {n, 0, z}]  (* A240059 *)
t5 = Table[Count[f[n], p_ /; Count[p, 1] >= Count[p, 3]], {n, 0, z}] (* A240059(n+1) *)

Crossrefs

Cf. A182714, A240058, A000041.

Sequence in context: A098507 A097066 A035548 * A288766 A348324 A007988

Adjacent sequences: A240056 A240057 A240058 * A240060 A240061 A240062

Keyword

nonn,easy

Author

Clark Kimberling, Mar 31 2014

Status

approved