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A184331
Table read by antidiagonals: T(n,k) = number of distinct n X k toroidal 0..6 arrays.
4
7, 28, 28, 119, 637, 119, 616, 19684, 19684, 616, 3367, 721525, 4484039, 721525, 3367, 19684, 28249228, 1153450872, 1153450872, 28249228, 19684, 117655, 1153470437, 316504102999, 2077059243301, 316504102999, 1153470437, 117655, 720916
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.
FORMULA
T(n,k) = (1/(n*k)) * Sum_{c|n} Sum_{d|k} phi(c) * phi(d) * 7^(n*k/lcm(c,d)). - Andrew Howroyd, Sep 27 2017
EXAMPLE
Table starts
7 28 119 616 3367 19684
28 637 19684 721525 28249228 1153470437
119 19684 4484039 1153450872 316504102999 90467424400444
616 721525 1153450872 2077059243301
3367 28249228 316504102999
19684 1153470437
117655
MATHEMATICA
T[n_, k_] := (1/(n*k))*Sum[Sum[EulerPhi[c]*EulerPhi[d]*7^(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) * 7^(n*k/lcm(c, d)))); \\ Andrew Howroyd, Sep 27 2017
CROSSREFS
Columns 1-3 are A054626, A184329, A184330.
Sequence in context: A300529 A299468 A200974 * A267432 A155712 A015817
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 11 2011
STATUS
approved