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A241388 Number of partitions p of n such that the number of distinct parts is not a part and max(p) - min(p) is a part. 5
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 5, 2, 7, 10, 15, 14, 30, 28, 49, 56, 81, 89, 135, 148, 212, 246, 327, 377, 506, 578, 759, 883, 1119, 1314, 1651, 1918, 2388, 2789, 3429, 4012, 4880, 5688, 6883, 8029, 9618, 11213, 13388, 15550, 18464, 21431, 25316, 29343 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

LINKS

Table of n, a(n) for n=0..53.

FORMULA

a(n) + A241387(n) + A241389(n) = A241391(n) for n >= 0.

EXAMPLE

a(9) counts this one partition:  63.

MATHEMATICA

z = 40; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := d[p] = Length[DeleteDuplicates[p]];

Table[Count[f[n], p_ /; MemberQ[p, d[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241387 *)

Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241388 *)

Table[Count[f[n], p_ /; MemberQ[p, d[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241389 *)

Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241390 *)

Table[Count[f[n], p_ /; MemberQ[p, d[p]] || MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241391 *)

CROSSREFS

Cf. A241387, A241389, A241390, A241391.

Sequence in context: A200646 A198130 A309773 * A305574 A248259 A128666

Adjacent sequences:  A241385 A241386 A241387 * A241389 A241390 A241391

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 21 2014

STATUS

approved

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Last modified October 1 17:45 EDT 2020. Contains 337444 sequences. (Running on oeis4.)