A086759 Permanent of the Cayley addition table of Z_{n}. a(n) is the permanent of the n X n matrix M_(i,j) = ((i+j) mod n) where i and j range from 0 to n-1.
0, 1, 9, 164, 5050, 227508, 14064519, 1146668608, 119249333028, 15400125776000, 2417814003691405, 453536611741073664, 100178077459552487070, 25735749696251388478720, 7608415981499790110521875, 2564724413131659780025106432, 977834710569917222742633274504
Offset: 1
Keywords
Examples
a(9) is the permanent of the matrix 0 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 0 2 3 4 5 6 7 8 0 1 3 4 5 6 7 8 0 1 2 4 5 6 7 8 0 1 2 3 5 6 7 8 0 1 2 3 4 6 7 8 0 1 2 3 4 5 7 8 0 1 2 3 4 5 6 8 0 1 2 3 4 5 6 7
Links
- Stefano Spezia, Table of n, a(n) for n = 1..36
- Robert Connelly, Maurice Pierre, Maximally Dense Disc Packings on the Plane, arXiv:1907.03652 [math.MG], 2019.
Programs
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Mathematica
Array[With[{s = Range[0, #]}, Permanent@ Array[RotateLeft[s, #] &, Last@ s + 1, 0]] &, 16, 0] (* Michael De Vlieger, Sep 03 2019 *) -
PARI
permRWNb(a)=n=matsize(a)[1];if(n==1,return(a[1,1]));sg=1;in=vectorv(n);x=in;x=a[,n]-sum(j=1,n,a[,j])/2;p=prod(i=1,n,x[i]);for(k=1,2^(n-1)-1,sg=-sg;j=valuation(k,2)+1;z=1-2*in[j];in[j]+=z;x+=z*a[,j];p+=prod(i=1,n,x[i],sg));return(2*(2*(n%2)-1)*p) for(n=1,21,a=matrix(n,n,i,j,((i+j-2)%n));print1(permRWNb(a)",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 14 2007
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PARI
a(n) = matpermanent(matrix(n, n, i, j, (i+j-2) % n)) \\ Stefano Spezia, Oct 25 2020
Extensions
a(9) from Neven Juric (neven.juric(AT)apis-it.hr), Jul 11 2005
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 14 2007
a(17) from Michael De Vlieger, Sep 03 2019