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0, 0, 0, 0, 2, 10, 30, 70, 140, 252, 420, 660, 990, 1430, 2002, 2730, 3640, 4760, 6120, 7752, 9690, 11970, 14630, 17710, 21252, 25300, 29900, 35100, 40950, 47502, 54810, 62930, 71920, 81840, 92752
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Also number of ways to insert two pairs of parentheses into a string of n-4 letters (allowing empty pairs of parentheses). E.g. there are 30 ways for 2 letters. Cf. A002415.
2,10,30,70, ... gives orchard crossing number of complete graph K_n. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 28 2003
If Y is a 2-subset of an n-set X then, for n>=4, a(n-1) is the number of 4-subsets and 5-subsets of X having exactly one element in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 28 2007
Middle column of table on Feder and Garber p.6. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 23 2009]
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REFERENCES
| Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 449.
S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.
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LINKS
| M. Aganagic, A. Klemm and C. Vafa, Disk Instantons, Mirror Symmetry and the Duality Web
D. Garber, [math/0303317] The Orchard crossing number of an abstract graph
Elie Feder, David Garber, The Orchard crossing number of an abstract graph, v2, Apr 23, 2009 [From Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 23 2009]
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FORMULA
| a(n) = A096338(2*n-6) = 2 *A000332(n), n>2. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 08 2010]
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MAPLE
| [seq(binomial(n, 4)*2, n=0..40)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 18 2006
seq(sum(sum(sum(k, j=0..k), k=0..m), m=1..n), n=-3..31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 26 2008
a:=n->add(binomial(n, 2)+add(binomial(n, 2), j=0..n), j=0..n):seq(a(n)/6, n=-2..30); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 27 2008]
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MATHEMATICA
| s1=s2=s3=s4=0; lst={0, 0, 0}; Do[a=n+(n+2); s1+=a; s2+=s1; s3+=s2; s4+=s3; AppendTo[lst, s3], {n, -1, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 04 2009]
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CROSSREFS
| A diagonal of A088617.
Cf. A033487, A050534, A060008.
Partial sums of A007290.
Sequence in context: A034262 A180499 A167214 * A051667 A106355 A120546
Adjacent sequences: A034824 A034825 A034826 * A034828 A034829 A034830
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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