A114530 a(n) = permanent of a bordered n X n (1,-1)-matrix with the following property: the elements on the border are 1; if we concatenate the rows of the matrix to form a vector v of length n^2, v_i = -1 if i is not a prime. The border of a matrix consists of the first and the last row and the first and the last column.

6, 0, 8, 144, -80, -384, -2816, -15360, -125184, 5322240, -22966272, 36771840, -887224320, 1488936960, -217760382976, -1484266291200, -45948014198784, 65021593190400, -3267216288645120, -856122753024000, -3180322010587725824

Offset: 3

Author

Simone Severini, Feb 15 2006

Keywords

• sign

Links

• Simone Severini, Home page

Programs

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=3,23,a=matrix(n,n,i,j,if(i==1||j==1||i==n||j==n,1,-1+2*isprime((i-1)*n+j)));print1(permRWNb(a)","))
\\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 15 2007

Extensions

More terms (and corrected definition) from Herman Jamke (hermanjamke(AT)fastmail.fm), May 15 2007