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A243841 Pair deficit of the most equal partition of n into two parts using ceiling rounding of the expectations of n, floor(n/2) and n-floor(n/2), assuming equal likelihood of states defined by the number of 2-cycles. 1
0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,41

COMMENTS

A162970 and A000085 provide the numerator and the denominator for calculating the expected value.

LINKS

Table of n, a(n) for n=0..53.

FORMULA

a(n) = ceiling(a162970(n)/a000085(n)) - (ceiling(a162970(floor(n/2))/a000085(floor(n/2))) + ceiling(a162970(n-floor(n/2))/a000085(n-floor(n/2))))

EXAMPLE

Trivially, for n =0,1 no pairs are possible so a(0) and a(1) are 0. For n = 2, the expectation, E(n), equals 0.5.  So a(2) = Ceiling(E(2))-(Ceiling(E(1))+Ceiling(E(1))) = 1.  For n=5 = 2 + 3, E(5) = 20/13, E(2) = 0.5 and E(3) = 0.75 and a(5) = Ceiling(E(5))- (Ceiling(E(2))+ Ceiling(E(3))) = 0

Interestingly, for n = 8, E(8) = 532/191 and E(4) = 6/5, so a(n) = 3 - (2 + 2)  = -1.

CROSSREFS

Cf. A000085, A162970.

Sequence in context: A016366 A016427 A326170 * A131038 A016353 A016398

Adjacent sequences:  A243838 A243839 A243840 * A243842 A243843 A243844

KEYWORD

sign

AUTHOR

Rajan Murthy, Jun 12 2014

STATUS

approved

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Last modified June 28 21:04 EDT 2022. Contains 354907 sequences. (Running on oeis4.)