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A080838
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Orchard crossing number of complete bipartite graph K_{1,n}.
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3
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0, 0, 0, 2, 5, 12, 21, 36, 54, 80, 110, 150, 195, 252, 315, 392, 476, 576, 684, 810, 945, 1100, 1265, 1452, 1650, 1872, 2106, 2366, 2639, 2940, 3255, 3600, 3960, 4352, 4760, 5202, 5661, 6156, 6669, 7220, 7790, 8400, 9030, 9702, 10395, 11132, 11891
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OFFSET
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1,4
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COMMENTS
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Also the minimum number of transitive triples in a tournament on n nodes, i.e., a(n) = C(n,3) - A006918(n-2). - Leen Droogendijk, Nov 10 2014
a(n) = the number of binary strings of length n+1 with exactly one pair of adjacent 0's and exactly two pairs of adjacent 1's. - Jeremy Dover, Jul 07 2016
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LINKS
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FORMULA
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a(n) = (n/16) * (2*n^2 - 8*n + 7 + (-1)^n).
G.f.: (x^5 + 2*x^4) / (1-x)^4 / (1+x)^2.
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MATHEMATICA
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CoefficientList[Series[(x^4 + 2 x^3) / (1 - x)^4 / (1 + x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, May 17 2013 *)
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PROG
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(PARI) for(n=1, 100, print1(if(n%2, n*(n-1)*(n-3)/8, n*(n-2)^2/8)", "))
(Magma) [n/16*(2*n^2 - 8*n + 7 + (-1)^n): n in [1..50]]; // Vincenzo Librandi, May 17 2013
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CROSSREFS
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Essentially partial sums of A211539.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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