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Search: id:A000943
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| A000943 |
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Number of combinatorial types of simplicial n-dimensional polytopes with n+3 nodes.
(Formerly M1352 N0519)
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+0
9
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| 1, 2, 5, 8, 18, 29, 57, 96, 183, 318, 604, 1080, 2047, 3762, 7145, 13354, 25471, 48164, 92193, 175780, 337581, 647313, 1246849, 2400828, 4636375, 8956045, 17334785, 33570800, 65108045, 126355319, 245492226, 477284164, 928772631, 1808538336
(list; graph; listen)
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OFFSET
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1,2
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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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
B. Gr\"{u}nbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.
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MAPLE
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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));
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MATHEMATICA
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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 ] ]
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CROSSREFS
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Cf. A049337, A000944.
Sequence in context: A024460 A039658 A063675 this_sequence A152006 A032063 A037233
Adjacent sequences: A000940 A000941 A000942 this_sequence A000944 A000945 A000946
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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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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