Search: id:A005040
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%I A005040 M1851
%S A005040 1,1,2,8,33,194,1196,8196,58140,427975,3223610,24780752,193610550,
%T A005040 1534060440,12302123640,99699690472,815521503060,6725991120004,
%U A005040 55882668179880
%N A005040 Number of dissections of a polygon.
%D A005040 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005040 F. Harary, E. M. Palmer and R. C. Read, On the cell-growth problem for 
               arbitrary polygons, Discr. Math. 11 (1975), 371-389.
%D A005040 E. V. Konstantinova, A survey of the cell-growth problem and some its 
               variations, preprint, 2001.
%H A005040 E. V. Konstantinova, <a href="http://com2mac.postech.ac.kr/">Com2Mac 
               - Preprints</a>
%F A005040 See Mathematica code.
%t A005040 p=5; Table[(Binomial[(p-1)n, n]/(((p-2)n+1)((p-2)n+2)) + If[OddQ[n], 
               If[OddQ[p], Binomial[(p-1)n/2, (n-1)/2]/n, (p+1)Binomial[((p-1)n-1)/
               2, (n-1)/2]/((p-2)n+2)], 3Binomial[(p-1)n/2, n/2]/((p-2)n+2)]+Plus 
               @@ Map[EulerPhi[ # ]Binomial[((p-1)n+1)/#, (n-1)/# ]/((p-1)n+1)&, 
               Complement[Divisors[GCD[p, n-1]], {1, 2}]])/2, {n, 1, 20}] - Robert 
               A. Russell (russell(AT)post.harvard.edu), Dec 11 2004
%Y A005040 Cf. A005419, A004127, A005036, A000207.
%Y A005040 Sequence in context: A150888 A030977 A030821 this_sequence A026577 A111643 
               A000163
%Y A005040 Adjacent sequences: A005037 A005038 A005039 this_sequence A005041 A005042 
               A005043
%K A005040 nonn,more
%O A005040 1,3
%A A005040 N. J. A. Sloane (njas(AT)research.att.com).
%E A005040 More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Oct 13 
               2001

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