A059736 A class of polytopal spheres.

0, 0, 1, 0, 1, 1, 4, 6, 16, 25, 52, 89, 175, 308, 593, 1066, 2031, 3743, 7124, 13330, 25445, 48134, 92160, 175743, 337541, 647269, 1246802, 2400776, 4636319, 8955984, 17334720, 33570730, 65107971, 126355239, 245492141, 477284073

Offset: 1

Author

N. J. A. Sloane, Feb 09 2001

Keywords

• nonn
• easy

Links

• V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

Programs

Maple

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:

Mathematica

a[n_] := (1/2)*(2^Quotient[n - 1, 2] + Total[(Mod[#, 2]*EulerPhi[#]*2^(n/#) &) /@ Divisors[n]]/(2*n)) - Floor[n^2/12] - 1;
Array[a, 36] (* Jean-François Alcover, Aug 30 2019 *)

Formula

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

Extensions

More terms from James Sellers, Feb 20 2001