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A344717
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a(n) = (3n - 9/2 - 1/n + 6/(n+1))*binomial(2n-2,n-1).
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2
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6, 34, 169, 791, 3576, 15807, 68783, 295867, 1261468, 5341128, 22487906, 94244294, 393439840, 1637091585, 6792664635, 28115240595, 116120791380, 478689505140, 1969993524510, 8095052323410, 33218808108720, 136148925337230, 557389537873974, 2279607910207326
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OFFSET
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2,1
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COMMENTS
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Conjecture: These are the number of linear intervals in the tilting posets of type B_n. An interval is linear if it is isomorphic to a total order. The conjecture has been checked up to the term 295867 for n = 9.
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LINKS
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MATHEMATICA
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Array[(3 # - 9/2 - 1/# + 6/(# + 1))*Binomial[2 # - 2, # - 1] &, 24, 2] (* Michael De Vlieger, Jan 17 2024, after Sage *)
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PROG
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(Sage)
def a(n):
return (3*n-9/2-1/n+6/(n+1))*binomial(2*n-2, n-1)
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CROSSREFS
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For the tilting posets of type A, see A344136.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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