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A241091     Number of partitions p of n into distinct parts such that max(p) <= 1 + 2*(number of parts of p). 3
0, 1, 1, 2, 1, 2, 3, 3, 3, 4, 5, 5, 7, 7, 9, 10, 11, 12, 15, 16, 19, 22, 24, 27, 30, 34, 37, 43, 47, 53, 59, 66, 72, 82, 88, 99, 109, 120, 131, 146, 160, 176, 194, 212, 233, 256, 279, 304, 334, 362, 396, 431, 471, 510, 558, 604, 659, 714, 776, 839, 913, 985 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..61.

FORMULA

a(n) = A241086(n) + A241092(n) for n >= 0.

EXAMPLE

a(12) counts these 5 partitions:  741, 732, 651, 642, 6321, 543, 5421.

MATHEMATICA

z = 30; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];

Table[Count[f[n], p_ /; Max[p] < 1 + 2*Length[p]], {n, 0, z}] (*A241086*)

Table[Count[f[n], p_ /; Max[p] <= 1 + 2*Length[p]], {n, 0, z}](*A241091*)

Table[Count[f[n], p_ /; Max[p] == 1 + 2*Length[p]], {n, 0, z}](*A241092*)

Table[Count[f[n], p_ /; Max[p] >= 1 + 2*Length[p]], {n, 0, z}](*A241089*)

Table[Count[f[n], p_ /; Max[p] > 1 + 2*Length[p]], {n, 0, z}] (*A241093*)

CROSSREFS

Cf. A241086, A241092, A241093.

Sequence in context: A240873 A208882 A186519 * A137719 A029165 A035431

Adjacent sequences:  A241088 A241089 A241090 * A241092 A241093 A241094

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 18 2014

STATUS

approved

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Last modified October 23 04:06 EDT 2021. Contains 348211 sequences. (Running on oeis4.)