A184290 Number of distinct n X 3 toroidal 0..5 arrays.

76, 7826, 1119936, 181402676, 31345666736, 5642220395616, 1044616697187576, 197432555854243976, 37907050706575921296, 7369130657373455467336, 1447029292717527455513576, 286511799958073253432316896, 57126045037793735333314420176

Offset: 1

Author

R. H. Hardin, Jan 10 2011

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100

Crossrefs

Column 3 of A184291.

Programs

Mathematica

T[n_, k_] := (1/(n*k))*Sum[Sum[EulerPhi[c]*EulerPhi[d]*6^(n*(k/LCM[c, d])), {d, Divisors[k]}], {c, Divisors[n]}]; a[n_] := T[n, 3]; Array[a, 13] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *)

PARI

a(n) = my(k=3); (1/(n*k)) * sumdiv(n, c, sumdiv(k, d, eulerphi(c) * eulerphi(d) * 6^(n*k/lcm(c, d)))); \\ Michel Marcus, Nov 01 2017

Extensions

Terms a(7) and beyond from Andrew Howroyd, Sep 27 2017