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Euler characteristics of polytopes.
(Formerly M1357)
0

%I M1357 #20 Jan 28 2018 07:24:02

%S 1,1,0,2,5,9,14,20,69,125,209,329,923,1715,3002,5004,12869,24309,

%T 43757,75581,184755,352715,646645,1144065,2704155,5200299,9657699,

%U 17383859,40116599

%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 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.

%F Numbers suggest that for n>3, a(n) = C(n, [n/2])-1 if (n mod 4)=0 or 1 and C(n, [n/2]-1)-1 otherwise. - _Ralf Stephan_, Jun 07 2005

%o (PARI) a(n)=if(n<3,(n==0||n==1), if(n<4,2,-1+if(n%4==0||n%4==1, binomial(n,n\2), binomial(n,n\2-1)))) \\ _Ralf Stephan_, Jun 07 2005

%K nonn

%O 1,4

%A _N. J. A. Sloane_