A241735 Number of partitions p = [x(1), ..., x(k)], where x(1) >= x(2) >= ... >= x(k), of n such that max(x(i) - x(i-1)) is a part of p.

0, 0, 0, 1, 1, 2, 4, 5, 7, 10, 15, 19, 28, 34, 46, 61, 81, 101, 137, 168, 218, 273, 349, 431, 550, 676, 849, 1043, 1298, 1579, 1959, 2373, 2913, 3526, 4301, 5178, 6293, 7544, 9109, 10895, 13091, 15591, 18666, 22158, 26402, 31269, 37120, 43813, 51853, 61027

Offset

0,6

Links

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

Formula

a(n) + A241736(n) = A000041(n) for n >= 0.

Example

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

Mathematica

z = 55; f[n_] := f[n] = IntegerPartitions[n]; g[p_] := Max[-Differences[p]];  g1[p_] := Min[-Differences[p]];
Table[Count[f[n], p_ /; MemberQ[p, g[p]]], {n, 0, z}]   (* A241735 *)
Table[Count[f[n], p_ /; ! MemberQ[p, g[p]]], {n, 0, z}] (* A241736 *)
Table[Count[f[n], p_ /; MemberQ[p, g1[p]]], {n, 0, z}]  (* A241760 *)
Table[Count[f[n], p_ /; ! MemberQ[p, g1[p]]], {n, 0, z}](* A241761 *)

Crossrefs

Cf. A241736, A241760, A241761, A000041.

Sequence in context: A018301 A351390 A218074 * A092295 A277102 A168639

Adjacent sequences: A241732 A241733 A241734 * A241736 A241737 A241738

Keyword

nonn,easy

Author

Clark Kimberling, Apr 28 2014

Status

approved