A241832 - OEIS

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A241832

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 parts of p.

8

0, 0, 0, 0, 0, 1, 1, 3, 3, 6, 7, 12, 14, 22, 27, 37, 46, 63, 76, 101, 124, 160, 196, 250, 302, 382, 463, 574, 693, 855, 1026, 1255, 1503, 1823, 2178, 2626, 3123, 3749, 4447, 5305, 6274, 7458, 8790, 10405, 12231, 14422, 16909, 19871, 23229, 27217, 31742

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OFFSET

0,8

LINKS

Table of n, a(n) for n=0..50.

FORMULA

a(n) = A241831(n) - A241830(n).

a(n) + A241828(n) + A241830(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts this single partition: 51.

MATHEMATICA

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

Table[Count[f[n], p_ /; g[p] < Length[p]], {n, 0, z}] (* A241828 *)

Table[Count[f[n], p_ /; g[p] <= Length[p]], {n, 0, z}] (* A241829 *)

Table[Count[f[n], p_ /; g[p] == Length[p]], {n, 0, z}] (* A241830 *)

Table[Count[f[n], p_ /; g[p] >= Length[p]], {n, 0, z}] (* A241831 *)

Table[Count[f[n], p_ /; g[p] > Length[p]], {n, 0, z}] (* A241832 *)

CROSSREFS

Cf. A241828, A241829, A241830, A241831, A000041.

Sequence in context: A088571 A325834 A365924 * A027187 A056508 A050065

Adjacent sequences: A241829 A241830 A241831 * A241833 A241834 A241835

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 30 2014

STATUS

approved