A241382 Number of partitions p of n such that the number of parts is a part and max(p) - min(p) is a part.

0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 3, 3, 6, 4, 10, 8, 12, 12, 20, 17, 29, 28, 45, 48, 68, 69, 98, 103, 134, 148, 194, 208, 271, 298, 377, 424, 528, 589, 735, 825, 1004, 1139, 1381, 1551, 1874, 2116, 2528, 2869, 3401, 3848, 4559, 5165, 6066, 6891, 8060, 9136

Offset

0,7

Links

Table of n, a(n) for n=0..55.

Formula

a(n) + A241383(n) + A241384(n) = A241386(n) for n >= 0.

Example

a(9) counts these 2 partitions:  432, 4311.

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. A241383, A241384, A241385, A241386.

Sequence in context: A201079 A318601 A306814 * A049260 A273294 A053186

Adjacent sequences: A241379 A241380 A241381 * A241383 A241384 A241385

Keyword

nonn,easy

Author

Clark Kimberling, Apr 21 2014

Status

approved