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A058861
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Number of 3-connected rooted cubic planar maps with n faces and girth at least 4.
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2
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0, 0, 1, 3, 12, 59, 313, 1713, 9559, 54189, 311460, 1812281, 10661303, 63336873, 379601353, 2293205687, 13953099573, 85451824382, 526431271347, 3260689089300, 20296848348929, 126918850161182, 796981464813540
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,4
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COMMENTS
| Number of 3-connected triangle-free rooted cubic maps with n faces.
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REFERENCES
| 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
| Z. Gao and N. C. Wormald, Enumeration of rooted cubic planar maps
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FORMULA
| G.f.=x^2*(1-3*x)*g, where g is defined by (x^3-3x^2+3x-1)g^4+(4x^4-12x^3+9x^2+2x-3)g^3+(6x^5-10x^4-15x^3+36x^2-14x-3)g^2+(4x^6+4x^5-45x^4+82x^3-59x^2+14x-1)g+x^7+5x^6-8x^5+x^4=0.
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MAPLE
| eq:=(x^3-3*x^2+3*x-1)*g^4+(4*x^4-12*x^3+9*x^2+2*x-3)*g^3+(6*x^5-10*x^4-15*x^3+36*x^2-14*x-3)*g^2+(4*x^6+4*x^5-45*x^4+82*x^3-59*x^2+14*x-1)*g+x^7+5*x^6-8*x^5+x^4: g:=sum(A[j]*x^j, j=1..37): for n from 1 to 37 do A[n]:=solve(coeff(expand(eq), x^n)=0) od: C3:=x^2*(1-3*x)*g: C3ser:=series(C3, x=0, 34): seq(coeff(C3ser, x^n), n=6..30);
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CROSSREFS
| Cf. A000260, A058859, A058860.
Sequence in context: A003316 A126959 A181328 * A105668 A192768 A179325
Adjacent sequences: A058858 A058859 A058860 * A058862 A058863 A058864
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 06 2001; revised Feb 17 2006
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EXTENSIONS
| G.f., program and more terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 30 2005
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