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 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. 0

%I #6 Mar 30 2012 18:54:34

%S 6,0,8,144,-80,-384,-2816,-15360,-125184,5322240,-22966272,36771840,

%T -887224320,1488936960,-217760382976,-1484266291200,-45948014198784,

%U 65021593190400,-3267216288645120,-856122753024000,-3180322010587725824

%N 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.

%H Simone Severini, <a href="http://www-users.york.ac.uk/~ss54">www-users.york.ac.uk/~ss54</a>

%o (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

%K sign

%O 3,1

%A _Simone Severini_, Feb 15 2006

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

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Last modified July 15 19:27 EDT 2024. Contains 374334 sequences. (Running on oeis4.)