Search: id:A000943
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%I A000943 M1352 N0519
%S A000943 1,2,5,8,18,29,57,96,183,318,604,1080,2047,3762,7145,13354,25471,48164,
%T A000943 92193,175780,337581,647313,1246849,2400828,4636375,8956045,17334785,
%U A000943 33570800,65108045,126355319,245492226,477284164,928772631,1808538336
%N A000943 Number of combinatorial types of simplicial n-dimensional polytopes with 
               n+3 nodes.
%D A000943 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000943 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000943 B. Gr\"{u}nbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.
%p A000943 with(numtheory); n := 50; for d from 2 to n do C(d) := 0; for h from 
               1 to d+3 do if (h mod 2 = 1) and (d+3 mod h = 0) then C(d) := C(d) 
               + phi(h) * 2^((d+3)/h); fi; od; C(d) := 2^(floor(d/2)) - floor ((d+4)/
               2) + C(d)/(4*(d+3)); od: A000943 := n-> eval(C(n));
%t A000943 a[ n_ ] := 2^Floor[ n/2 ]-Floor[ (n+4)/2 ]+(1/(4*(n+3)))*Plus@@Map[ EulerPhi[ 
               # ]*2^((n+3)/#)&, Select[ Divisors[ n+3 ], OddQ ] ]
%Y A000943 Cf. A049337, A000944.
%Y A000943 Sequence in context: A024460 A039658 A063675 this_sequence A152006 A032063 
               A037233
%Y A000943 Adjacent sequences: A000940 A000941 A000942 this_sequence A000944 A000945 
               A000946
%K A000943 nonn,nice
%O A000943 1,2
%A A000943 N. J. A. Sloane (njas(AT)research.att.com).
%E A000943 n=12 term corrected (typo in reference), formula (due to Perles) and 
               more terms from Lukas Finschi (finschi(AT)ifor.math.ethz.ch), Mar 
               06 2001

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