A241821 - OEIS

A241821

Number of partitions p = [x(1), ..., x(k)], where x(1) >= x(2) >= ... >= x(k), of n such that max(x(i) - x(i-1)) >= number of distinct parts of p.

0, 0, 0, 0, 1, 2, 4, 6, 10, 13, 22, 29, 40, 55, 76, 95, 129, 167, 215, 278, 354, 448, 570, 716, 896, 1115, 1387, 1713, 2116, 2597, 3182, 3881, 4741, 5748, 6976, 8416, 10177, 12219, 14704, 17592, 21051, 25101, 29960, 35559, 42267, 50017, 59253, 69898, 82524

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OFFSET

0,6

LINKS

Table of n, a(n) for n=0..48.

FORMULA

a(n) = A241820(n) + A241822(n) for n >= 0.

a(n) + A241818(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 4 partitions: 51, 42, 411, 3111.

MATHEMATICA

z = 30; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := d[p] = Length[DeleteDuplicates[p]]; g[p_] := Max[-Differences[p]];