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A080838 Orchard crossing number of complete bipartite graph K_{1,n}. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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 0s and exactly two pairs of adjacent 1s. - Jeremy Dover, Jul 07 2016

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

D. Garber, The Orchard crossing number of an abstract graph, arXiv:math/0303317 [math.CO], 2003.

M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.

FORMULA

a(n) = n/16*(2n^2-8n+7+(-1)^n). G.f.: (x^5+2x^4)/(1-x)^4/(1+x)^2.

For n odd, a(n) = A060423(n). - Gerald McGarvey, Sep 14 2008

MATHEMATICA

CoefficientList[Series[(x^4 + 2 x^3) / (1 - x)^4 / (1 + x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, May 17 2013 *)

Table[n/16*(2 n^2 - 8 n + 7 + (-1)^n), {n, 47}] (* Michael De Vlieger, Aug 01 2016 *)

PROG

(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

CROSSREFS

Third column of A274228. - Jeremy Dover, Jul 07 2016

Sequence in context: A327065 A307605 A079648 * A244396 A182993 A238741

Adjacent sequences:  A080835 A080836 A080837 * A080839 A080840 A080841

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Mar 28 2003

STATUS

approved

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Last modified August 24 03:51 EDT 2019. Contains 326260 sequences. (Running on oeis4.)