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A241823 Number of partitions p = [x(1), ..., x(k)], where x(1) >= x(2) >=  ... >= x(k), of n such that min(x(i) - x(i-1)) < number of distinct parts of p. 6
0, 0, 1, 2, 3, 5, 8, 12, 18, 26, 37, 51, 70, 94, 126, 166, 219, 284, 369, 473, 607, 770, 977, 1228, 1544, 1925, 2399, 2970, 3673, 4517, 5550, 6784, 8284, 10073, 12232, 14799, 17883, 21536, 25903, 31064, 37204, 44439, 53015, 63090, 74987, 88932, 105337 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..46.

FORMULA

a(n) = A241821(n) - A241820(n) for n >= 0.

a(n) + A241818(n) + A241820(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 2 partitions:  51, 411

MATHEMATICA

z = 30; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := d[p] = Length[DeleteDuplicates[p]]; g1[p_] := Min[-Differences[p]]

Table[Count[f[n], p_ /; g1[p] < d[p]], {n, 0, z}]  (* A241823 *)

Table[Count[f[n], p_ /; g1[p] <= d[p]], {n, 0, z}] (* A241824 *)

Table[Count[f[n], p_ /; g1[p] == d[p]], {n, 0, z}] (* A241825 *)

Table[Count[f[n], p_ /; g1[p] >= d[p]], {n, 0, z}] (* A241826 *)

Table[Count[f[n], p_ /; g1[p] > d[p]], {n, 0, z}]  (* A241827 *)

CROSSREFS

Cf. A241824, A241825, A241826, A241827, A000041.

Sequence in context: A039901 A173564 A121946 * A058984 A084376 A098693

Adjacent sequences:  A241820 A241821 A241822 * A241824 A241825 A241826

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 30 2014

STATUS

approved

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Last modified May 18 04:22 EDT 2021. Contains 343994 sequences. (Running on oeis4.)