The On-Line Encyclopedia of Integer Sequences (OEIS)

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A241085

Number of partitions p of n into distinct parts such that max(p) < 2*(number of parts of p).
(history; published version)

#7 by N. J. A. Sloane at Thu Apr 24 10:28:53 EDT 2014

STATUS

proposed

approved

#6 by Clark Kimberling at Wed Apr 23 17:04:40 EDT 2014

STATUS

editing

proposed

#5 by Clark Kimberling at Thu Apr 17 11:34:12 EDT 2014

MATHEMATICA

Table[Count[f[n], p_ /; Max[p] == 2*Length[p]], {n, 0, z}] (* A241085 A241087 *)

#4 by Clark Kimberling at Thu Apr 17 11:30:28 EDT 2014

MATHEMATICA

Table[Count[f[n], p_ /; Max[p] < 2*Length[p]], {n, 0, z}] (* A241085 *)

Table[Count[f[n], p_ /; Max[p] <= 2*Length[p]], {n, 0, z}] (* A241086 *)

Table[Count[f[n], p_ /; Max[p] == 2*Length[p]], {n, 0, z}] (* A241075 A241085 *)

Table[Count[f[n], p_ /; Max[p] >= 2*Length[p]], {n, 0, z}] (* A241088 *)

Table[Count[f[n], p_ /; Max[p] > 2*Length[p]], {n, 0, z}] (* A241089 *)

#3 by Clark Kimberling at Thu Apr 17 11:27:00 EDT 2014

NAME

allocated for Clark Kimberling Number of partitions p of n into distinct parts such that max(p) < 2*(number of parts of p).

DATA

0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 3, 2, 3, 3, 4, 5, 6, 6, 7, 8, 8, 10, 11, 13, 14, 17, 18, 21, 22, 25, 27, 31, 33, 38, 42, 47, 52, 57, 63, 69, 76, 82, 91, 99, 109, 119, 132, 142, 158, 171, 188, 203, 223, 240, 263, 284, 309, 334, 364, 393, 428, 463, 501, 543, 588

OFFSET

0,9

EXAMPLE

a(15) counts these 5 partitions: 7521, 7431, 6531, 6432, 54321.

MATHEMATICA

z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];

Table[Count[f[n], p_ /; Max[p] < 2*Length[p]], {n, 0, z}] (* A241085 *)

Table[Count[f[n], p_ /; Max[p] <= 2*Length[p]], {n, 0, z}] (* A241086 *)

Table[Count[f[n], p_ /; Max[p] == 2*Length[p]], {n, 0, z}] (* A241075 *)

Table[Count[f[n], p_ /; Max[p] >= 2*Length[p]], {n, 0, z}] (* A241088 *)

Table[Count[f[n], p_ /; Max[p] > 2*Length[p]], {n, 0, z}] (* A241089 *)

CROSSREFS

Cf. A241086, A241087, A241088, A241089.

KEYWORD

allocated

nonn,easy

AUTHOR

Clark Kimberling, Apr 17 2014

STATUS

approved

editing

#2 by Clark Kimberling at Tue Apr 15 20:46:16 EDT 2014

KEYWORD

allocating

allocated

#1 by Clark Kimberling at Tue Apr 15 20:46:16 EDT 2014

NAME

allocated for Clark Kimberling

KEYWORD

allocating

STATUS

approved