A241272 -id:A241272 - cp's OEIS frontend

A241063 Number of partitions p of n into distinct parts such that max(p) = 3*min(p).

0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 1, 0, 1, 3, 2, 1, 1, 3, 2, 2, 3, 4, 3, 3, 5, 4, 5, 5, 7, 7, 7, 7, 7, 9, 10, 10, 11, 13, 14, 14, 14, 15, 17, 19, 22, 24, 23, 24, 28, 28, 31, 32, 36, 39, 42, 43, 46, 49, 53, 56, 59, 65, 68, 73, 77, 81, 87, 92

Offset: 0

Clark Kimberling, Apr 18 2014

			a(12) counts these 2 partitions:  93, 642.

Cf. A241035, A241069, A241272, A241273.

z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
    Table[Count[f[n], p_ /; Max[p] == 2*Min[p]], {n, 0, z}] (* A241035 *)
    Table[Count[f[n], p_ /; Max[p] == 3*Min[p]], {n, 0, z}] (* A241063 *)
    Table[Count[f[n], p_ /; Max[p] == 4*Min[p]], {n, 0, z}] (* A241069 *)
    Table[Count[f[n], p_ /; Max[p] == 5*Min[p]], {n, 0, z}] (* A241272 *)
    Table[Count[f[n], p_ /; Max[p] == 6*Min[p]], {n, 0, z}] (* A241273 *)

A241069 Number of partitions p of n into distinct parts such that max(p) = 4*min(p).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 0, 1, 1, 2, 1, 2, 1, 3, 4, 3, 3, 3, 4, 6, 6, 4, 6, 5, 8, 8, 9, 9, 10, 13, 11, 13, 15, 17, 20, 21, 21, 24, 25, 29, 30, 33, 35, 40, 44, 44, 49, 51, 56, 61, 66, 69, 77, 82, 91, 95, 102, 106, 116, 127, 134, 147, 157, 168, 182

Offset: 0

Clark Kimberling, Apr 18 2014

			a(10) counts these 2 partitions:  82, 4321.

Cf. A241035, A241063, A241272, A241273.

z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
    Table[Count[f[n], p_ /; Max[p] == 2*Min[p]], {n, 0, z}] (* A241035 *)
    Table[Count[f[n], p_ /; Max[p] == 3*Min[p]], {n, 0, z}] (* A241063 *)
    Table[Count[f[n], p_ /; Max[p] == 4*Min[p]], {n, 0, z}] (* A241069 *)
    Table[Count[f[n], p_ /; Max[p] == 5*Min[p]], {n, 0, z}] (* A241272 *)
    Table[Count[f[n], p_ /; Max[p] == 6*Min[p]], {n, 0, z}] (* A241273 *)

A241273 Number of partitions p of n into distinct parts such that max(p) = 6*min(p).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 3, 1, 2, 2, 2, 2, 1, 4, 2, 3, 3, 5, 5, 6, 8, 8, 9, 10, 13, 14, 16, 18, 20, 20, 24, 25, 28, 31, 36, 37, 40, 42, 46, 51, 55, 62, 65, 72, 76, 83, 89, 98, 107, 117, 126, 139, 149, 163, 177, 195, 208, 226, 247, 267, 291

Offset: 0

Clark Kimberling, Apr 18 2014

			a(14) counts these 3 partitions:  {12,2}, {6,5,2,1}, {6,4,3,1}.

Cf. A241035, A241063, A241269, A241272.

z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
Table[Count[f[n], p_ /; Max[p] == 2*Min[p]], {n, 0, z}] (* A241035 *)
Table[Count[f[n], p_ /; Max[p] == 3*Min[p]], {n, 0, z}] (* A241063 *)
Table[Count[f[n], p_ /; Max[p] == 4*Min[p]], {n, 0, z}] (* A241069 *)
Table[Count[f[n], p_ /; Max[p] == 5*Min[p]], {n, 0, z}] (* A241272 *)
Table[Count[f[n], p_ /; Max[p] == 6*Min[p]], {n, 0, z}] (* A241273 *)

cp's OEIS Frontend

A241063 Number of partitions p of n into distinct parts such that max(p) = 3*min(p).

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A241069 Number of partitions p of n into distinct parts such that max(p) = 4*min(p).

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A241273 Number of partitions p of n into distinct parts such that max(p) = 6*min(p).

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