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A241386 Number of partitions p of n such that the number of parts is a part or max(p) - min(p) is a part. 5
0, 1, 0, 1, 2, 4, 4, 8, 10, 15, 19, 24, 35, 45, 57, 76, 98, 123, 161, 198, 252, 313, 388, 472, 597, 722, 891, 1085, 1332, 1602, 1964, 2348, 2852, 3412, 4109, 4889, 5879, 6964, 8317, 9846, 11706, 13795, 16358, 19226, 22695, 26630, 31305, 36621, 42966, 50116 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..49.

FORMULA

a(n) + A241385(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 4 partitions:  42, 321, 2211, 21111.

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, A241384, A241385.

Sequence in context: A073117 A039879 A125204 * A265204 A073420 A034408

Adjacent sequences:  A241383 A241384 A241385 * A241387 A241388 A241389

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 21 2014

STATUS

approved

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Last modified October 31 05:06 EDT 2020. Contains 338098 sequences. (Running on oeis4.)