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A241086     Number of partitions p of n into distinct parts such that max(p) <= 2*(number of parts of p). 8
0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 5, 5, 6, 7, 8, 9, 11, 12, 14, 15, 17, 19, 21, 24, 27, 31, 34, 38, 42, 47, 51, 57, 62, 70, 77, 85, 93, 104, 114, 125, 137, 150, 164, 180, 196, 214, 234, 255, 279, 304, 332, 360, 393, 426, 464, 502, 545, 589, 640, 691, 749 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..62.

FORMULA

a(15) counts these 7 partitions:  8421, 7521, 7431, 654, 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}] (* A241087 *)

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. A241085, A241087, A241088, A241089.

Sequence in context: A269850 A036054 A029102 * A194818 A029081 A168656

Adjacent sequences:  A241083 A241084 A241085 * A241087 A241088 A241089

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 17 2014

STATUS

approved

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Last modified December 9 09:37 EST 2021. Contains 349627 sequences. (Running on oeis4.)