A263830 The number c_{Z^3,pi_1(B_2)}(2n) of 3-torus 2n-coverings over the second amphicosm.

1, 5, 9, 23, 19, 53, 33, 93, 74, 119, 73, 255, 99, 213, 219, 363, 163, 482, 201, 581, 393, 485, 289, 1085, 422, 663, 634, 1047, 451, 1463, 513, 1417, 897, 1103, 915, 2374, 723, 1365, 1227, 2511, 883, 2661, 969, 2399, 2078, 1973, 1153, 4419

Offset: 1

Author

N. J. A. Sloane, Oct 28 2015

Keywords

• nonn

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..20000
• G. Chelnokov, M. Deryagina, A. Mednykh, On the Coverings of Amphicosms; Revised title: On the coverings of Euclidian manifolds B_1 and B_2, arXiv preprint arXiv:1502.01528 [math.AT], 2015.

Crossrefs

Cf. A263825-A263830, A263832.

Programs

Mathematica

a[n_] := 1/2 Sum[Sum[(d^2 + 3/2 + 1/2 (-1)^Mod[d, 2] + (-1)^Mod[Quotient[n, d m], 2] + (-1)^Mod[d+Quotient[n, d m], 2])m, {m, Divisors[Quotient[n, d] ]}], {d, Divisors[n]}];
Array[a, 48] (* Jean-François Alcover, Sep 16 2018, after Gheorghe Coserea *)

PARI

a(n) = {
  1/2 * sumdiv(n, d, sumdiv(n\d, m,
  (sqr(d) + 3/2 + 1/2*(-1)^(d%2) + (-1)^((n\(d*m))%2) +
  (-1)^((d + n\(d*m))%2)) * m));
};
vector(48, n, a(n))  \\ Gheorghe Coserea, May 05 2016

Extensions

More terms from Gheorghe Coserea, May 05 2016