OFFSET
1,1
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 31 terms from R. H. Hardin)
S. N. Ethier, Counting toroidal binary arrays, arXiv:1301.2352v1 [math.CO], Jan 10, 2013.
S. N. Ethier and Jiyeon Lee, Counting toroidal binary arrays, II, arXiv:1502.03792v1 [math.CO], Feb 12, 2015.
Veronika Irvine, Lace Tessellations: A mathematical model for bobbin lace and an exhaustive combinatorial search for patterns, PhD Dissertation, University of Victoria, 2016.
FORMULA
T(n,k) = (1/(n*k)) * Sum_{c|n} Sum_{d|k} phi(c) * phi(d) * 6^(n*k/lcm(c,d)). - Andrew Howroyd, Sep 27 2017
EXAMPLE
Table starts
6 21 76 336 1560 7826 39996
21 351 7826 210456 6047412 181410426 5597460306
76 7826 1119936 181402676 31345666736 5642220395616
336 210456 181402676 176319685116
1560 6047412 31345666736
7826 181410426
39996
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]}]; Table[T[n-k+1, k], {n, 1, 8}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 30 2017, after Andrew Howroyd *)
PROG
(PARI)
T(n, k) = (1/(n*k)) * sumdiv(n, c, sumdiv(k, d, eulerphi(c) * eulerphi(d) * 6^(n*k/lcm(c, d)))); \\ Andrew Howroyd, Sep 27 2017
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 10 2011
STATUS
approved