A241761 Number of partitions p = [x(1), ..., x(k)], where x(1) >= x(2) >= ... >= x(k), of n such that min(x(i) - x(i-1)) is not a part of p.

1, 1, 2, 2, 5, 7, 9, 14, 20, 28, 39, 54, 71, 96, 127, 167, 220, 286, 368, 473, 604, 766, 970, 1219, 1528, 1907, 2373, 2939, 3634, 4472, 5489, 6715, 8198, 9972, 12109, 14658, 17711, 21340, 25669, 30796, 36890, 44082, 52594, 62613, 74435, 88303, 104613, 123698

Offset

0,3

Comments

The partition {n} is included in the count.

Links

Table of n, a(n) for n=0..47.

Formula

a(n) + A241760(n) = A000041(n) for n >= 0.

Example

a(6) counts these 6 partitions:  6, 51, 411, 33, 3111, 222, 2211, 21111, 111111.

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. A241735, A241736, A241761, A000041.

Sequence in context: A188623 A256358 A308842 * A278388 A239737 A262883

Adjacent sequences: A241758 A241759 A241760 * A241762 A241763 A241764

Keyword

nonn,easy

Author

Clark Kimberling, Apr 28 2014

Status

approved