cp's OEIS Frontend

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.

%I A114530 #12 May 06 2025 09:28:11
%S A114530 6,0,8,144,-80,-384,-2816,-15360,-125184,5322240,-22966272,36771840,
%T A114530 -887224320,1488936960,-217760382976,-1484266291200,-45948014198784,
%U A114530 65021593190400,-3267216288645120,-856122753024000,-3180322010587725824
%N 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.
%H A114530 Simone Severini, <a href="https://web.archive.org/web/20040816115828/http://www-users.york.ac.uk/~ss54/">Home page</a>
%o A114530 (PARI)
%o A114530 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)
%o A114530 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)","))
%o A114530 \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 15 2007
%K A114530 sign
%O A114530 3,1
%A A114530 _Simone Severini_, Feb 15 2006
%E A114530 More terms (and corrected definition) from Herman Jamke (hermanjamke(AT)fastmail.fm), May 15 2007