A240077 Number of partitions of n such that m(greatest part) <= m(1), where m = multiplicity.

1, 1, 1, 2, 3, 4, 7, 9, 14, 19, 28, 36, 53, 68, 94, 122, 165, 210, 280, 354, 462, 583, 749, 936, 1192, 1481, 1862, 2303, 2871, 3527, 4366, 5336, 6555, 7977, 9737, 11790, 14317, 17260, 20845, 25033, 30093, 35993, 43087, 51348, 61216, 72711, 86362, 102236

Offset

0,4

Links

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

Formula

a(n) = A240076(n) + A240078(n) for n >= 0.

Example

a(7) counts these 9 partitions:  61, 511, 421, 4111, 3211, 31111, 22111, 211111, 1111111.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Count[p, Max[p]] < Count[p, 1]], {n, 0, z}]  (* A240076 *)
t2 = Table[Count[f[n], p_ /; Count[p, Max[p]] <= Count[p, 1]], {n, 0, z}] (* A240077 *)
t3 = Table[Count[f[n], p_ /; Count[p, Max[p]] == Count[p, 1]], {n, 0, z}] (* A240078 *)
t4 = Table[Count[f[n], p_ /; Count[p, Max[p]] > Count[p, 1]], {n, 0, z}] (* A117995 *)
t5 = Table[Count[f[n], p_ /; Count[p, Max[p]] >= Count[p, 1]], {n, 0, z}] (* A240080 *)

Crossrefs

Cf. A240076, A240078, A117995, A240080.

Sequence in context: A238495 A239329 A094093 * A237997 A317885 A321535

Adjacent sequences: A240074 A240075 A240076 * A240078 A240079 A240080

Keyword

nonn,easy

Author

Clark Kimberling, Apr 01 2014

Status

approved