login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A146558 Number of order n permutations without collinear triples modulo n. 1
1, 2, 0, 16, 0, 72, 0, 256, 0, 0, 0, 2304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..29.

L. Li, Collinear triples in permutations, arXiv:0802.0572 [math.CO], 2008.

FORMULA

For prime p>=3, a(p) = 0.

EXAMPLE

For n=4, there are a(4)=16 permutations without collinear triples: [1, 2, 4, 3], [1, 3, 2, 4], [1, 3, 4, 2], [1, 4, 2, 3], [2, 1, 3, 4], [2, 3, 1, 4], [2, 4, 1, 3], [2, 4, 3, 1], [3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 4, 1], [3, 4, 2, 1], [4, 1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2]

PROG

(PARI) { a(n) = local(p, r, g); r=0; for(j=1, n!, p=numtoperm(n, j); g=1; forvec(v=vector(3, i, [1, n]), if(matdet([1, v[1], p[v[1]]; 1, v[2], p[v[2]]; 1, v[3], p[v[3]]])%n==0, g=0; break), 2); if(g, r++)); r }

CROSSREFS

Cf. A135538, A146557.

Sequence in context: A074031 A086261 A111978 * A025600 A009006 A155585

Adjacent sequences:  A146555 A146556 A146557 * A146559 A146560 A146561

KEYWORD

nonn,hard,more

AUTHOR

Max Alekseyev, Nov 01 2008

EXTENSIONS

Edited by Max Alekseyev, Jun 21 2010

a(14)-a(29) from Bert Dobbelaere, Mar 15 2020

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 November 30 05:31 EST 2020. Contains 338781 sequences. (Running on oeis4.)