login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A184284 Table read by antidiagonals: T(n,k) = number of distinct n X k toroidal 0..2 arrays. 13
3, 6, 6, 11, 27, 11, 24, 130, 130, 24, 51, 855, 2211, 855, 51, 130, 5934, 44368, 44368, 5934, 130, 315, 44487, 956635, 2691711, 956635, 44487, 315, 834, 341802, 21524790, 174342216, 174342216, 21524790, 341802, 834, 2195, 2691675, 498112275 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

....3........6..........11...........24............51...........130

....6.......27.........130..........855..........5934.........44487

...11......130........2211........44368........956635......21524790

...24......855.......44368......2691711.....174342216...11767964475

...51.....5934......956635....174342216...33891544611.6863038218842

..130....44487....21524790..11767964475.6863038218842

..315...341802...498112275.817028472960

..834..2691675.11767920118

.2195.21524542

.5934

LINKS

Alois P. Heinz, antidiagonals n = 1..50, flattened (first 58 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) * 3^(n*k/lcm(c,d)). - Andrew Howroyd, Sep 27 2017

MATHEMATICA

T[n_, k_] := (1/(n*k))*Sum[EulerPhi[c]*EulerPhi[d]*3^(n*k/LCM[c, d]), {c, Divisors[n]}, {d, Divisors[k]}]; Table[T[n-k+1, k], {n, 1, 9}, {k, 1, n}] // Flatten (*Jean-François Alcover, Oct 07 2017, after Andrew Howroyd *)

PROG

(PARI)

T(n, k) = (1/(n*k)) * sumdiv(n, c, sumdiv(k, d, eulerphi(c) * eulerphi(d) * 3^(n*k/lcm(c, d)))); \\ Andrew Howroyd, Sep 27 2017

CROSSREFS

Columns 1-6 are A001867, A184279, A184280, A184281, A184282, A184283.

Main diagonal is A184278.

Cf. A184271, A184277, A184288, A184291, A184331, A184294 (0..1, 0..3 etc.).

Sequence in context: A132384 A201155 A200534 * A287882 A066297 A160713

Adjacent sequences:  A184281 A184282 A184283 * A184285 A184286 A184287

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 10 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 24 06:56 EDT 2019. Contains 321444 sequences. (Running on oeis4.)