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A241384 Number of partitions p of n such that the number of parts is a part and max(p) - min(p) is not a part. 5
0, 1, 0, 0, 1, 2, 0, 4, 3, 5, 5, 9, 8, 17, 14, 26, 29, 43, 46, 71, 76, 109, 120, 162, 185, 251, 285, 375, 440, 560, 653, 831, 967, 1209, 1417, 1743, 2045, 2505, 2925, 3553, 4166, 5014, 5864, 7040, 8213, 9798, 11431, 13555, 15795, 18671, 21693, 25536, 29651 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..52.

FORMULA

a(n) + A241382(n) + A241383(n) = A241386(n) for n >= 0.

EXAMPLE

a(9) counts these 5 partitions:  72, 531, 51111, 4221, 333.

MATHEMATICA

z = 40; f[n_] := f[n] = IntegerPartitions[n];

Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241382 *)

Table[Count[f[n],  p_ /; ! MemberQ[p, Length[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241383 *)

Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241384 *)

Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241385 *)

Table[Count[f[n], p_ /; MemberQ[p, Length[p]] || MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241386 *)

CROSSREFS

Cf. A241382, A241383, A241385, A241386.

Sequence in context: A324471 A122512 A128263 * A140254 A204187 A095202

Adjacent sequences:  A241381 A241382 A241383 * A241385 A241386 A241387

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 21 2014

STATUS

approved

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Last modified August 14 09:14 EDT 2020. Contains 336480 sequences. (Running on oeis4.)