proposed

approved

editing

proposed

Number of partitions p of n into distinct parts such that max(p) >= -1 + 2*min(p).

Table[Count[f[n], p_ /; Max[p] <= -1 + 2*Min[p]], {n, 0, z}] (* A241066A240874 *)

Table[Count[f[n], p_ /; Max[p] > -1 + 2*Min[p]], {n, 0, z}] (* A241069A241036 *)

Cf. A241065, A241066A240874, A241067, A241069A241036.

allocated Number of partitions p of n into distinct parts forsuch Clarkthat Kimberlingmax(p) >= -1 + 2*min(p).

0, 1, 0, 1, 1, 2, 3, 3, 5, 6, 8, 10, 13, 15, 20, 23, 29, 35, 42, 49, 60, 71, 84, 98, 116, 135, 158, 184, 214, 248, 286, 329, 380, 436, 500, 572, 654, 745, 848, 965, 1094, 1242, 1406, 1588, 1794, 2023, 2278, 2563, 2881, 3234, 3626, 4063, 4546, 5083, 5677

0,6

a(8) counts these 5 partitions: 71, 62, 53, 521, 431.

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}] (* A241066 *)

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}] (* A241069 *)

Cf. A241065, A241066, A241067, A241069.

allocated

nonn,easy

Clark Kimberling, Apr 16 2014

approved

editing

allocated for Clark Kimberling

allocated

approved