A238546 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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}]