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A243840 Pair deficit of the most equal in size partition of n into two parts using floor rounding of the expectations for n, floor(n/2) and n- floor(n/2), assuming equal likelihood of states defined by the number of two-cycles. 1
0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 3, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 1, 2, 2, 2, 1, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

LINKS

Table of n, a(n) for n=0..79.

FORMULA

a(n) = floor(a162970(n)/a000085(n)) - floor(a162970(floor(n/2))/a000085(floor(n/2))) - floor(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) = Floor(E(2))-Floor(E(1))-Floor(E(1)) = 0.  For n=5 = 2 + 3, E(5) = 20/13, E(2) = 0.5 and E(3) = 0.75 and a(5) = Floor(E(5))-Floor(E(2))-Floor(E(3)) = 1.

Interestingly, for n = 8, E(8) = 532/191 and E(4) = 6/5, so a(n) = 2 - 1 -1  = 0.

CROSSREFS

A162970 provides the numerator for calculating the expected value.

A000085 provides the denominator for calculating the expected value.

Sequence in context: A113193 A239110 A278514 * A117898 A212810 A072344

Adjacent sequences:  A243837 A243838 A243839 * A243841 A243842 A243843

KEYWORD

nonn

AUTHOR

Rajan Murthy, Jun 12 2014

STATUS

approved

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Last modified June 27 19:20 EDT 2022. Contains 354898 sequences. (Running on oeis4.)