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A059736 A class of polytopal spheres.

%I A059736 #18 Jul 02 2025 16:02:00
%S A059736 0,0,1,0,1,1,4,6,16,25,52,89,175,308,593,1066,2031,3743,7124,13330,
%T A059736 25445,48134,92160,175743,337541,647269,1246802,2400776,4636319,
%U A059736 8955984,17334720,33570730,65107971,126355239,245492141,477284073
%N A059736 A class of polytopal spheres.
%H A059736 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 A059736 a(n) = A007147(n) - [n^2/12] - 1.
%p A059736 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 A059736 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 A059736 Array[a, 36] (* _Jean-François Alcover_, Aug 30 2019 *)
%K A059736 nonn,easy
%O A059736 1,7
%A A059736 _N. J. A. Sloane_, Feb 09 2001
%E A059736 More terms from _James Sellers_, Feb 20 2001