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A class of polytopal spheres.
1

%I #17 Aug 30 2019 05:29:16

%S 0,0,1,0,1,1,4,6,16,25,52,89,175,308,593,1066,2031,3743,7124,13330,

%T 25445,48134,92160,175743,337541,647269,1246802,2400776,4636319,

%U 8955984,17334720,33570730,65107971,126355239,245492141,477284073

%N A class of polytopal spheres.

%H V. A. Liskovets, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/LISK/Derseq.html">Some easily derivable sequences</a>, J. Integer Sequences, 3 (2000), #00.2.2.

%F a(n) = A007147(n) - [n^2/12] - 1.

%p A016116 := n->2^floor(n/2):with(numtheory): A000016 := proc(n) local d,t1: if n = 0 then RETURN(1) else t1 := 0; for d from 1 to n do if n mod d = 0 and d mod 2 = 1 then t1 := t1+phi(d)*2^(n/ d)/(2*n); fi; od; RETURN(t1); fi; end: A007147 := n->1/2*(A016116(n-1)+A000016(n)): A059736 := n->A007147(n) - floor(n^2/12) - 1: for j from 1 to 100 do printf(`%d,`, A059736(j)) od:

%t a[n_] := (1/2)*(2^Quotient[n - 1, 2] + Total[(Mod[#, 2]*EulerPhi[#]*2^(n/#) &) /@ Divisors[n]]/(2*n)) - Floor[n^2/12] - 1;

%t Array[a, 36] (* _Jean-François Alcover_, Aug 30 2019 *)

%K nonn,easy

%O 1,7

%A _N. J. A. Sloane_, Feb 09 2001

%E More terms from _James A. Sellers_, Feb 20 2001