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.

1, 132, 1460808, 6357011889600, 44491520971919463292800, 2082476039060691409777705387034081280, 2712373659248840873249840585282508476815021942277876736, 410721884168854528740774423430429149549703377187068577398353854503625738636800

Offset

2,2

Comments

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

Links

Table of n, a(n) for n=2..9.

Example

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

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)
a(n) = permRWNb(matrix(n, n, i, j, fibonacci((i-1)*n+j-1))); \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 15 2007
(PARI) a(n) = matpermanent(matrix(n, n, i, j, fibonacci((i-1)*n+j-1))); \\ Michel Marcus, Apr 08 2025

Crossrefs

Sequence in context: A321975 A289568 A368024 * A147692 A028674 A369820

Adjacent sequences: A114531 A114532 A114533 * A114535 A114536 A114537

Keyword

nonn

Author

Simone Severini, Feb 15 2006

Extensions

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

Status

approved