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A006481 Euler characteristics of polytopes.
(Formerly M0533)
3

%I M0533 #32 Oct 26 2018 13:35:33

%S 1,2,3,4,5,11,21,36,57,127,253,463,793,1717,3433,6436,11441,24311,

%T 48621,92379,167961,352717,705433,1352079,2496145,5200301,10400601,

%U 20058301,37442161

%N Euler characteristics of polytopes.

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

%H Vincenzo Librandi, <a href="/A006481/b006481.txt">Table of n, a(n) for n = 1..1000</a>

%H H. Hadwiger and P. Mani, <a href="https://doi.org/10.1016/0097-3165(74)90099-5">On polyhedra with extremal Euler characteristic</a>, J. Combin. Theory, A 17 (1974), 345-349. See p. 346.

%F Numbers suggest that for n not divisible by 4, a(n) = C(n, [n/2]) + 1 and C(n, [(n-1)/2]) + 1 otherwise (see A051920 and A037952+1). - _Ralf Stephan_, Jun 07 2005

%t a[n_] := Binomial[n-1, 2*Floor[(n-1)/4] + 1] + 1; Table[a[n], {n, 1, 29}] (* _Jean-François Alcover_, Jan 23 2012, after _Ralf Stephan_ *)

%Y Very like A051920. Cf. A320996.

%K nonn,nice

%O 1,2

%A _N. J. A. Sloane_

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