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A241819 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. 5
1, 1, 2, 3, 5, 6, 9, 11, 17, 20, 30, 37, 50, 64, 84, 106, 141, 178, 224, 290, 368, 457, 574, 722, 894, 1113, 1371, 1693, 2082, 2555, 3108, 3806, 4630, 5605, 6787, 8197, 9881, 11877, 14256, 17047, 20395, 24320, 28958, 34409, 40867, 48333, 57243, 67548, 79683 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

a(n) + A241822(n) = A000041(n) for n >= 0.

EXAMPLE

a(6)= 9 counts all of the 11 partitions of 6 except 51, 411.

MATHEMATICA

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

Table[Count[f[n], p_ /; g[p] < d[p]], {n, 0, z}]  (* A241818 *)

Table[Count[f[n], p_ /; g[p] <= d[p]], {n, 0, z}] (* A241819 *)

Table[Count[f[n], p_ /; g[p] == d[p]], {n, 0, z}] (* A241820 *)

Table[Count[f[n], p_ /; g[p] >= d[p]], {n, 0, z}] (* A241821 *)

Table[Count[f[n], p_ /; g[p] > d[p]], {n, 0, z}]  (* A241822 *)

CROSSREFS

Cf. A241818, A241820, A241821, A241822, A000041.

Sequence in context: A224956 A131995 A060714 * A227070 A032718 A086191

Adjacent sequences:  A241816 A241817 A241818 * A241820 A241821 A241822

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 30 2014

STATUS

approved

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Last modified May 30 10:30 EDT 2020. Contains 334724 sequences. (Running on oeis4.)