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A241093

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

0, 0, 0, 0, 1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 13, 17, 21, 26, 31, 38, 45, 54, 65, 77, 92, 108, 128, 149, 175, 203, 237, 274, 318, 366, 424, 486, 559, 640, 733, 836, 953, 1084, 1232, 1398, 1583, 1792, 2025, 2286, 2576, 2902, 3262, 3666, 4111, 4610, 5160, 5774

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OFFSET

0,8

LINKS

Table of n, a(n) for n=0..55.

FORMULA

a(n) + A241086(n) + A241093(n) = A000009(n) for n >= 1.

EXAMPLE

a(12) counts these 8 partitions: {12}, {11,1}, {10,2}, {9,3}, {9,2,1}, {8,4}, {8,3,1}, {7,5}.

MATHEMATICA

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*)