A240853 Number of partitions p of n into distinct parts including 2*min(p).

0, 0, 0, 1, 0, 0, 2, 1, 1, 3, 2, 3, 5, 5, 7, 8, 9, 12, 16, 16, 19, 27, 29, 34, 42, 47, 55, 66, 77, 89, 105, 117, 136, 162, 182, 209, 242, 274, 313, 360, 405, 463, 530, 595, 675, 765, 860, 970, 1099, 1233, 1384, 1559, 1743, 1954, 2191, 2445, 2734, 3057, 3403

Offset

0,7

Links

Table of n, a(n) for n=0..58.

Formula

a(n) + A240854(n) = A000009(n) for n >= 0.

Example

a(9) counts these 3 partitions:  63, 621, 432.

Mathematica

z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
    Table[Count[f[n], p_ /; MemberQ[p, 2*Min[p]]], {n, 0, z}]  (* A240853 *)
    Table[Count[f[n], p_ /; !MemberQ[p, 2*Min[p]]], {n, 0, z}] (* A240854 *)

Crossrefs

Cf. A240854, A000009.

Sequence in context: A347584 A366398 A365932 * A363094 A319849 A117334

Adjacent sequences: A240850 A240851 A240852 * A240854 A240855 A240856

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2014

Status

approved