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Search: id:A081616
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| A081616 |
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Sequence of constants appearing in formula for expected number of inversions after a sequence of random adjacent transpositions. |
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+0
1
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| 0, 0, 0, 1, 9, 69, 510, 3740, 27454, 202321, 1498074, 11145324, 83291428, 625022772, 4707757080, 35579447280, 269718129308, 2050317850201, 15625047614946, 119347362039788, 913501931766460, 7005437509949364, 53817428069374328, 414107216180618608
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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H. Eriksson, K. Ericcson and J. Sjostrand, Expected inversion number after k adjacent transpositions, in Formal Power Series and Algebraic Combinatorics, ed. D. Krob et al., Springer, 2000, pp. 677-685.
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LINKS
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N. Eriksen, Expected number of inversions after a sequence of random adjacent transpositions - an exact expression , Discr. Math., 298 (2005), 155-168.
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FORMULA
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See Maple code for formula (found by N. Eriksen).
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MAPLE
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A081616 := proc(n) local b, s, l; b := binomial; (1/2)*add( b(n-1, s-1)*(-1)^(s-1)*4^(n-s)*b(2*floor(s/2), floor(s/2))* add( l*b(2*ceil(s/2)-1, ceil(s/2)+l ), l=0..floor((s-1)/2) ), s=3..n); end;
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CROSSREFS
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Adjacent sequences: A081613 A081614 A081615 this_sequence A081617 A081618 A081619
Sequence in context: A072258 A125372 A075045 this_sequence A126530 A110202 A110201
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KEYWORD
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nonn
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AUTHOR
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njas, Apr 23 2003
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