cp's OEIS Frontend

A114534 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.

%I A114534 #14 Apr 09 2025 10:58:12
%S A114534 1,132,1460808,6357011889600,44491520971919463292800,
%T A114534 2082476039060691409777705387034081280,
%U A114534 2712373659248840873249840585282508476815021942277876736,410721884168854528740774423430429149549703377187068577398353854503625738636800
%N A114534 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 A114534 Conjecture: The rank of the matrix M is 2 for every n.
%e A114534 For n=2, M=[0,1;1,2];
%e A114534 For n=3, M=[0,1,1;2,3,5;8,13,21].
%o A114534 (PARI)
%o A114534 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 A114534 a(n) = permRWNb(matrix(n,n,i,j,fibonacci((i-1)*n+j-1))); \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 15 2007
%o A114534 (PARI) a(n) = matpermanent(matrix(n,n,i,j,fibonacci((i-1)*n+j-1))); \\ _Michel Marcus_, Apr 08 2025
%K A114534 nonn
%O A114534 2,2
%A A114534 _Simone Severini_, Feb 15 2006
%E A114534 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 15 2007