A114533 Permanent of the n X n matrix with numbers prime(1),prime(2),...,prime(n^2) in order across rows.

1, 2, 29, 3746, 1919534, 2514903732, 6571874957648, 30662862975835376, 228731722381012564816, 2641049525155781555257440, 43818773386947889568479502592, 1014966115357067575070490776083200, 31412851866841234377483875199638978304

Offset: 0

Author

Simone Severini, Feb 15 2006

Keywords

• nonn

Comments

Previous name was : "a(n) = permanent of the 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 prime number".

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..36 (terms 0..20 from Alois P. Heinz)

Crossrefs

Cf. A067276, A232773.

Programs

Maple

with(LinearAlgebra):
a:= n->`if`(n=0, 1, Permanent(Matrix(n, (i, j)->ithprime((i-1)*n+j)))):
seq(a(n), n=0..12);  # Alois P. Heinz, Dec 23 2013

Mathematica

a[n_] := Permanent[Table[Prime[(i-1)*n+j], {i, 1, n}, {j, 1, n}]]; a[0]=1; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 12}] (* Jean-François Alcover, Jan 07 2016, adapted from Maple *)
Join[{1},Table[Permanent[Partition[Prime[Range[n^2]],n]],{n,15}]] (* Harvey P. Dale, Aug 03 2019 *)

PARI

permRWN(a)=n=matsize(a)[1]; if(n==1,return(a[1,1])); n1=n-1; sg=1; m=1; nc=0; in=vector(n); x=in; for(i=1,n,x[i]=a[i,n]-sum(j=1,n,a[i,j])/2); p=prod(i=1,n,x[i]); while(m,sg=-sg; j=1; if((nc%2)!=0,j++; while(in[j-1]==0,j++)); in[j]=1-in[j]; z=2*in[j]-1; nc+=z; m=nc!=in[n1]; for(i=1,n,x[i]+=z*a[i,j]); p+=sg*prod(i=1,n,x[i])); return(2*(2*(n%2)-1)*p)
for(n=1,19,a=matrix(n,n,i,j,prime((i-1)*n+j)); print1(permRWN(a)", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 11 2007

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

PARI

{a(n) = matpermanent(matrix(n, n, i, j, prime((i-1)*n+j)))}
for(n=0, 25, print1(a(n), ", ")) \\ Vaclav Kotesovec, Aug 13 2021

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 11 2007

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

New name from Michel Marcus, Nov 30 2013

a(0) inserted and a(12) by Alois P. Heinz, Dec 23 2013