Search: a241093 -id:a241093
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A241091
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Number of partitions p of n into distinct parts such that max(p) <= 1 + 2*(number of parts of p).
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+10
3
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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
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graph;
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listen;
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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a(12) counts these 5 partitions: 741, 732, 651, 642, 6321, 543, 5421.
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MATHEMATICA
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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*)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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A241092
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Number of partitions p of n into distinct parts such that max(p) = 1 + 2*(number of parts of p).
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+10
3
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0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 7, 7, 8, 9, 10, 10, 12, 13, 15, 17, 19, 21, 25, 26, 29, 32, 35, 38, 42, 46, 51, 57, 62, 69, 76, 83, 90, 100, 107, 117, 127, 139, 150, 165, 178, 195, 212, 231, 250, 273, 294, 319, 346, 373, 402
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,13
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LINKS
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FORMULA
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EXAMPLE
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a(12) counts these 5 partitions: 741, 732, 651, 642, 6321, 543, 5421.
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MATHEMATICA
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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*)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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