A114534 - OEIS

%I #4 Mar 30 2012 18:54:34

%S 1,132,1460808,6357011889600,44491520971919463292800,

%T 2082476039060691409777705387034081280,

%U 2712373659248840873249840585282508476815021942277876736

%N The n-th entry of the sequence is the value of the permanent of an n X n matrix M defined as follows: if we concatenate the rows of M to form a vector v of length n^2, v_i is the i-th Fibonacci number.

%C Conjecture: The rank of the matrix M is 2 for every n.

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

%e For n=2, M=[0,1;1,0];

%e For n=3, M=[0,1,1;2,3,5;8,13,21].

%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,fibonacci((i-1)*n+j-1));print1(permRWNb(a)",")) - Herman Jamke (hermanjamke(AT)fastmail.fm), May 15 2007

%K nonn

%O 2,2

%A _Simone Severini_, Feb 15 2006

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