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

3,1

Links

Table of n, a(n) for n=3..23.

Simone Severini, www-users.york.ac.uk/~ss54

Prog

(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, 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

Crossrefs

Sequence in context: A201898 A193336 A240251 * A085673 A117492 A022903

Adjacent sequences: A114527 A114528 A114529 * A114531 A114532 A114533

Keyword

sign

Author

Simone Severini, Feb 15 2006

Extensions

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

Status

approved