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A000943 Number of combinatorial types of simplicial n-dimensional polytopes with n+3 nodes.
(Formerly M1352 N0519)
9
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; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

B. Gr├╝nbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..34.

MAPLE

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));

MATHEMATICA

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 ] ]

CROSSREFS

Cf. A049337, A000944.

Sequence in context: A024460 A039658 A063675 * A304966 A152006 A271619

Adjacent sequences:  A000940 A000941 A000942 * A000944 A000945 A000946

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved

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Last modified February 22 08:42 EST 2020. Contains 332133 sequences. (Running on oeis4.)