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A087457
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Number of odd length roads between any adjacent nodes in virtual optimal chordal ring of degree 3 (the length of chord < number of nodes/2).
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4
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1, 5, 31, 213, 1551, 11723, 90945, 719253, 5773279, 46889355, 384487665, 3177879675, 26442188865, 221278343445, 1860908156031, 15717475208853, 133256583398655, 1133591857814363, 9672323357640129, 82752014457666363
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 2nd ed. 1998, see page number?
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..100
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FORMULA
| From Michael Somos: a(1)=1; a(n) = 9*a(n-1) - 2*A086618(n); A086618(n) = sum(k=0, n, Catalan(n)*C(n, k)^2 ); where Catalan(n) = (2n)!/[n!(n+1)! ] and C(n, k) = n!/[k!(n-k)! ]
a(n)=A002893(n)/3 = (1/3)*Sum_{k=0..n}binomial(n,k)^2*binomial(2k,k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 14 2008]
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EXAMPLE
| a(1)=1; a(2)=9*a(1)-2*2=9-4=5; a(3)=9*5-2*7=31; a(4)=9*31-2*33=213; etc
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MAPLE
| a := 1; s := 0; for k from 1 to 10 do for i from 0 to k do ss := ((2*(i))!/((i)!*(i+1)!))*((k)!/((i)!*(k-i)!))^2; s := s+ss; od; a := (9*a-2*s); s := 0; od;
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CROSSREFS
| Cf. A086617, A086618.
Sequence in context: A002649 A104091 A153292 * A146962 A036758 A153232
Adjacent sequences: A087454 A087455 A087456 * A087458 A087459 A087460
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KEYWORD
| nonn
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AUTHOR
| B. Dubalski (dubalski(AT)atr.bydgoszcz.pl), Oct 23 2003
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