A238546 Number of partitions p of n such that floor(n/2) is not a part of p.

1, 1, 1, 3, 4, 8, 10, 17, 23, 35, 45, 66, 86, 120, 154, 209, 267, 355, 448, 585, 736, 946, 1178, 1498, 1857, 2335, 2875, 3583, 4389, 5428, 6611, 8118, 9846, 12013, 14498, 17592, 21147, 25525, 30558, 36711, 43791, 52382, 62259, 74173, 87879, 104303, 123179

Offset

1,4

Links

Giovanni Resta, Table of n, a(n) for n = 1..500

Formula

a(n) + A119620(n+1) = A000041(n), for n>1.

a(n) = p(n) - p(ceiling(n/2)) = A000041(n) - A000041(ceiling(n/2)), for n>1. - Giovanni Resta, Mar 02 2014

Example

a(6) counts all the 11 partitions of 6 except 33, 321, 3111.

Mathematica

Table[Count[IntegerPartitions[n], p_ /; !MemberQ[p, Floor[n/2]]], {n, 50}]

Crossrefs

Cf. A119620.

Sequence in context: A210631 A212543 A355193 * A147617 A308910 A308959

Adjacent sequences: A238543 A238544 A238545 * A238547 A238548 A238549

Keyword

nonn,easy

Author

Clark Kimberling, Feb 28 2014

Status

approved