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A006416
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Number of rooted planar maps. Also a(n)=T(4,n-3), array T as in A049600.
(Formerly M4490)
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2
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1, 8, 20, 38, 63, 96, 138, 190, 253, 328, 416, 518, 635, 768, 918, 1086, 1273, 1480, 1708, 1958, 2231, 2528, 2850, 3198, 3573, 3976, 4408, 4870, 5363, 5888, 6446, 7038, 7665, 8328, 9028, 9766, 10543, 11360, 12218, 13118, 14061, 15048
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OFFSET
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2,2
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COMMENTS
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If Y_i (i=1,2,3) are 2-blocks of an n-set X then, for n>=6, a(n-3) is the number of (n-3)-subsets of X intersecting each Y_i (i=1,2,3). - Milan Janjic, Nov 09 2007
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Walsh, T. R. S.; Lehman, A. B.; Counting rooted maps by genus. III: Nonseparable maps. J. Combinatorial Theory Ser. B 18 (1975), 222-259.
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LINKS
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T. D. Noe, Table of n, a(n) for n=2..1000
Milan Janjic, Two Enumerative Functions
_Simon Plouffe_, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
_Simon Plouffe_, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.: (1+4*x-6*x^2+2*x^3)/(1-x)^4.
a(n-3)=(1/6)*n^3-(1/2)*n^2-(8/3)*n+6, n=6,7,... - Milan Janjic, Nov 09 2007
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MAPLE
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A006416:=(1+4*z-6*z**2+2*z**3)/(z-1)**4; [Conjectured by Simon Plouffe in his 1992 dissertation.]
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MATHEMATICA
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f[n_]:=Sum[i+i^2-6, {i, 1, n}]/2; Table[f[n], {n, 3, 5!}] [From Vladimir Joseph Stephan Orlovsky, Mar 08 2010]
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CROSSREFS
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Sequence in context: A082231 A073607 A086062 * A192753 A121307 A086169
Adjacent sequences: A006413 A006414 A006415 * A006417 A006418 A006419
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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