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Search: id:A058859
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| A058859 |
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Number of 1-connected rooted cubic planar maps with n faces. |
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3
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| 1, 3, 19, 143, 1089, 8564, 69075, 569469, 4783377, 40829748, 353395155, 3096104105, 27415923905, 245069538465, 2209155012387, 20064713628389, 183478258249569, 1688112897834496, 15618577076864579, 145242456429736935
(list; graph; listen)
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OFFSET
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4,2
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REFERENCES
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Z. Gao and N. C. Wormald, Enumeration of rooted cubic planar maps, Annals of Combinatorics, 6 (2002), no. 3-4, 313-325.
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LINKS
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Z. Gao and N. C. Wormald, Enumeration of rooted cubic planar maps
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FORMULA
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G.f.=x^4*(1-2x-4x^2)m-2x^8*m^2, where m is defined by 16x^11*m^4+ (-24x^9+32x^8+72x^7)m^3+(-15x^7-108x^6-194x^5-92x^4+x^3)m^2+(-2x^5-33x^4-70x^3-46x^2+16x-1)m-x^2-11x+1=0
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MAPLE
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eq:=16*x^11*m^4+(-24*x^9+32*x^8+72*x^7)*m^3+(-15*x^7-108*x^6-194*x^5-92*x^4+x^3)\ *m^2+(-2*x^5-33*x^4-70*x^3-46*x^2+16*x-1)*m-x^2-11*x+1: m:=sum(A[j]*x^j, j=0..35): A[0]:=solve(subs(x=0, expand(eq))): for n from 1 to 35 do A[n]:=solve(coeff(expand(eq), x^n)=0) od: C:=(1-2*x-4*x^2)*x^4*m-2*x^8*m^2: Cser:=series(C, x=0, 30): seq(coeff(Cser, x^n), n=4..26); (Deutsch)
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CROSSREFS
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Cf. A000260, A058860, A058861.
Sequence in context: A025571 A082758 A110525 this_sequence A095002 A080833 A073516
Adjacent sequences: A058856 A058857 A058858 this_sequence A058860 A058861 A058862
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 06 2001; revised Feb 17 2006
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EXTENSIONS
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G.f., program and more terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 30 2005
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