Search: a241068 -id:a241068
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A241065
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Number of partitions p of n into distinct parts such that max(p) < -1 + 2*min(p).
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+10
3
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0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 4, 3, 3, 4, 5, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 10, 11, 10, 12, 12, 13, 14, 15, 16, 17, 19, 18, 20, 22, 22, 25, 26, 27, 29, 30, 32, 34, 36, 37, 41, 43, 44, 47, 50, 51, 55, 58, 60, 65, 68, 70, 75, 78, 82, 85, 91
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OFFSET
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0,8
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LINKS
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EXAMPLE
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a(17) counts these 3 partitions: {17}, {10, 7}, {9,8}.
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MATHEMATICA
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z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
Table[Count[f[n], p_ /; Max[p] < -1 + 2*Min[p]], {n, 0, z}] (* A241065 *)
Table[Count[f[n], p_ /; Max[p] <= -1 + 2*Min[p]], {n, 0, z}] (* A240874 *)
Table[Count[f[n], p_ /; Max[p] == -1 + 2*Min[p]], {n, 0, z}] (* A241067 *)
Table[Count[f[n], p_ /; Max[p] >= -1 + 2*Min[p]], {n, 0, z}] (* A241068 *)
Table[Count[f[n], p_ /; Max[p] > -1 + 2*Min[p]], {n, 0, z}] (* A241036 *)
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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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A241067
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Number of partitions p of n into distinct parts such that max(p) = -1 + 2*min(p).
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+10
3
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0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 0, 2, 1, 2, 1, 1, 1, 2, 2, 2, 3, 1, 1, 4, 2, 3, 4, 3, 3, 3, 3, 4, 6, 5, 4, 6, 4, 5, 7, 6, 7, 8, 8, 8, 9, 7, 8, 11, 11, 11, 13, 12, 12, 15, 12, 14, 17, 15, 18, 19, 20, 20
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,18
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LINKS
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EXAMPLE
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a(17) counts these 2 partitions: {11,6}, {7,6,4}.
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MATHEMATICA
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z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
Table[Count[f[n], p_ /; Max[p] < -1 + 2*Min[p]], {n, 0, z}] (* A241065 *)
Table[Count[f[n], p_ /; Max[p] <= -1 + 2*Min[p]], {n, 0, z}] (* A240874 *)
Table[Count[f[n], p_ /; Max[p] == -1 + 2*Min[p]], {n, 0, z}] (* A241067 *)
Table[Count[f[n], p_ /; Max[p] >= -1 + 2*Min[p]], {n, 0, z}] (* A241068 *)
Table[Count[f[n], p_ /; Max[p] > -1 + 2*Min[p]], {n, 0, z}] (* A241036 *)
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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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