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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, 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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 28 2014
STATUS
approved