A241383 Number of partitions p of n such that the number of parts is not a part and max(p) - min(p) is a part.

0, 0, 0, 0, 1, 2, 2, 4, 6, 8, 11, 12, 21, 24, 33, 42, 57, 68, 95, 110, 147, 176, 223, 262, 344, 402, 508, 607, 758, 894, 1117, 1309, 1614, 1905, 2315, 2722, 3306, 3870, 4657, 5468, 6536, 7642, 9113, 10635, 12608, 14716, 17346, 20197, 23770, 27597, 32334

Offset

0,6

Links

Table of n, a(n) for n=0..50.

Formula

a(n) + A241382(n) + A241384(n) = A241386(n) for n >= 0.

Example

a(9) counts these 8 partitions:  63, 3321, 32211, 321111, 22221, 222111, 221111, 2111111.

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, A241384, A241385, A241386.

Sequence in context: A116859 A179999 A286736 * A258125 A361394 A147982

Adjacent sequences: A241380 A241381 A241382 * A241384 A241385 A241386

Keyword

nonn,easy

Author

Clark Kimberling, Apr 21 2014

Status

approved