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

Author

Clark Kimberling, Feb 28 2014

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

Cf. A119620.

Programs

Mathematica

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

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