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Search: id:A131454
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| A131454 |
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2 up, 2 down, ..., 2 up, 2 down, 2up permutations of length 4n+3. |
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+0
4
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| 1, 71, 45541, 120686411, 908138776681, 15611712012050351, 531909061958526321421, 32491881630252866646683891, 3302814916156503291298772711761, 527393971346575736206847604137659031
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Bisection of A005981. The entries listed above suggest various congruences for a(n): a(n) = 1 (mod 10), a(n) = 1 + 70*n (mod 100), a(n) = 1 + 70*n + 200*n(n-1) (mod 1000). Are these congruences true for all n? For an arbitrary integer m, the sequence a(n) taken modulo m may eventually become periodic. Compare with A081727.
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LINKS
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B.Shapiro, A. Vainshtein, Counting real rational functions with all real critical values, Moscow Math. J., 3 (2003), 647-659.
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FORMULA
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E.g.f.:sum_ {n = 0 .. inf} a(n)*(x^(4n+3))/(4n+3)! = (exp(2x)-2*sin(x)*exp(x)-1)/(2*exp(x)+cos(x)*(exp(2x)+1)). It appears that a(n)= (4n+3)!*coefficient of x^(4n+3) in the Taylor expansion of -4/(2*exp(x)+cos(x)*(exp(2x)+1)).
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EXAMPLE
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(1 4 5 3 2 6 7) is a 2 up, 2 down, 2 up permutation - one of the seventy-one permutations of this type in the symmetric group on 7 letters.
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CROSSREFS
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Cf. A000111, A005981, A058257, A131453, A131455.
Sequence in context: A115447 A033527 A112615 this_sequence A099684 A078915 A144242
Adjacent sequences: A131451 A131452 A131453 this_sequence A131455 A131456 A131457
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KEYWORD
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easy,nonn
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AUTHOR
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Peter Bala (pbala(AT)toucansurf.com), Jul 13 2007
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