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A114533 Permanent of the n X n matrix with numbers prime(1),prime(2),...,prime(n^2) in order across rows. 5
1, 2, 29, 3746, 1919534, 2514903732, 6571874957648, 30662862975835376, 228731722381012564816, 2641049525155781555257440, 43818773386947889568479502592, 1014966115357067575070490776083200, 31412851866841234377483875199638978304 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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)
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 *)
PROG
(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
CROSSREFS
Sequence in context: A055559 A350858 A345041 * A180128 A367871 A087194
KEYWORD
nonn
AUTHOR
Simone Severini, Feb 15 2006
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
STATUS
approved

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Last modified July 14 03:51 EDT 2024. Contains 374291 sequences. (Running on oeis4.)