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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. 2
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

Alois P. Heinz, Table of n, a(n) for n = 0..20

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-Fran├žois 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

CROSSREFS

Cf. A232773.

Sequence in context: A252042 A295426 A345041 * A180128 A087194 A331427

Adjacent sequences:  A114530 A114531 A114532 * A114534 A114535 A114536

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 June 14 12:04 EDT 2021. Contains 345025 sequences. (Running on oeis4.)