A241760 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 a part of p.

0, 0, 0, 1, 0, 0, 2, 1, 2, 2, 3, 2, 6, 5, 8, 9, 11, 11, 17, 17, 23, 26, 32, 36, 47, 51, 63, 71, 84, 93, 115, 127, 151, 171, 201, 225, 266, 297, 346, 389, 448, 501, 580, 648, 740, 831, 945, 1056, 1201, 1340, 1517, 1695, 1910, 2130, 2399, 2670

Offset

0,7

Links

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

Formula

a(n) + A241761(n) = A000041(n) for n >= 0.

Example

a(6) counts these 2 partitions:  42, 321.

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: A085432 A029169 A202090 * A224493 A129193 A262446

Adjacent sequences: A241757 A241758 A241759 * A241761 A241762 A241763

Keyword

nonn,easy

Author

Clark Kimberling, Apr 28 2014

Status

approved