A241069 -id:A241069 - 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 *)

A241272 Number of partitions p of n into distinct parts such that max(p) = 5*min(p).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 0, 2, 1, 1, 2, 2, 2, 3, 3, 4, 6, 5, 5, 7, 7, 9, 11, 10, 11, 12, 12, 14, 18, 18, 18, 21, 21, 24, 27, 30, 30, 36, 37, 42, 47, 49, 54, 60, 64, 71, 81, 83, 91, 100, 107, 116, 129, 136, 147, 159, 172, 184, 200, 213, 228

Offset: 0

Clark Kimberling, Apr 18 2014

			a(12) counts these 2 partitions:  {10,2}, {5,4,2,1}.

Cf. A241035, A241063, A241269, 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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A241272 Number of partitions p of n into distinct parts such that max(p) = 5*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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