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A241093     Number of partitions p of n into distinct parts such that max(p) > 1 + 2*(number of parts of p). 3
0, 0, 0, 0, 1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 13, 17, 21, 26, 31, 38, 45, 54, 65, 77, 92, 108, 128, 149, 175, 203, 237, 274, 318, 366, 424, 486, 559, 640, 733, 836, 953, 1084, 1232, 1398, 1583, 1792, 2025, 2286, 2576, 2902, 3262, 3666, 4111, 4610, 5160, 5774 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..55.

FORMULA

a(n) + A241086(n) + A241093(n) = A000009(n) for n >= 1.

EXAMPLE

a(12) counts these 8 partitions:  {12}, {11,1}, {10,2}, {9,3}, 9,2,1}, {8,4}, {8,3,1}, {7,5}.

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, A241091, A241092, A000009.

Sequence in context: A080655 A199120 A118083 * A116470 A115649 A191168

Adjacent sequences:  A241090 A241091 A241092 * A241094 A241095 A241096

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 18 2014

STATUS

approved

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Last modified October 24 20:35 EDT 2021. Contains 348233 sequences. (Running on oeis4.)