A356490
a(n) is the determinant of a symmetric Toeplitz matrix M(n) whose first row consists of prime(1), prime(2), ..., prime(n).
Original entry on oeis.org
1, 2, -5, 12, -19, -22, 1143, -4284, 14265, -46726, -84405, 1306096, 32312445, 522174906, 4105967871, 5135940112, -642055973735, -2832632334858, 14310549077571, 380891148658140, 4888186898996125, -49513565563840210, 383405170118692791, -2517836083641473036, -3043377347606882055
Offset: 0
For n = 1 the matrix M(1) is
2
with determinant a(1) = 2.
For n = 2 the matrix M(2) is
2, 3
3, 2
with determinant a(2) = -5.
For n = 3 the matrix M(3) is
2, 3, 5
3, 2, 3
5, 3, 2
with determinant a(3) = 12.
-
A356490 := proc(n)
local T,c ;
if n =0 then
return 1 ;
end if;
T := LinearAlgebra[ToeplitzMatrix]([seq(ithprime(c),c=1..n)],n,symmetric) ;
LinearAlgebra[Determinant](T) ;
end proc:
seq(A356490(n),n=0..15) ; # R. J. Mathar, Jan 31 2023
-
k[i_]:=Prime[i]; M[ n_]:=ToeplitzMatrix[Array[k, n]]; a[n_]:=Det[M[n]]; Join[{1},Table[a[n],{n,24}]]
-
a(n) = matdet(apply(prime, matrix(n,n,i,j,abs(i-j)+1))); \\ Michel Marcus, Aug 12 2022
-
from sympy import Matrix, prime
def A356490(n): return Matrix(n,n,[prime(abs(i-j)+1) for i in range(n) for j in range(n)]).det() # Chai Wah Wu, Aug 12 2022
A356491
a(n) is the permanent of a symmetric Toeplitz matrix M(n) whose first row consists of prime(1), prime(2), ..., prime(n).
Original entry on oeis.org
1, 2, 13, 184, 4745, 215442, 14998965, 1522204560, 208682406913, 37467772675962, 8809394996942597, 2597094620811897948, 954601857873086235553, 428809643170145564168434, 229499307540038336275308821, 144367721963876506217872778284, 106064861375232790889279725340713
Offset: 0
For n = 1 the matrix M(1) is
2
with permanent a(1) = 2.
For n = 2 the matrix M(2) is
2, 3
3, 2
with permanent a(2) = 13.
For n = 3 the matrix M(3) is
2, 3, 5
3, 2, 3
5, 3, 2
with permanent a(3) = 184.
Cf.
A005843 (trace of the matrix M(n)),
A309131 (k-superdiagonal sum of the matrix M(n)),
A356483 (hafnian of the matrix M(2*n)),
A356490 (determinant of the matrix M(n)).
-
A356491 := proc(n)
local c ;
if n =0 then
return 1 ;
end if;
LinearAlgebra[ToeplitzMatrix]([seq(ithprime(c),c=1..n)],n,symmetric) ;
LinearAlgebra[Permanent](%) ;
end proc:
seq(A356491(n),n=0..15) ; # R. J. Mathar, Jan 31 2023
-
k[i_]:=Prime[i]; M[ n_]:=ToeplitzMatrix[Array[k, n]]; a[n_]:=Permanent[M[n]]; Join[{1},Table[a[n],{n,16}]]
-
a(n) = matpermanent(apply(prime, matrix(n,n,i,j,abs(i-j)+1))); \\ Michel Marcus, Aug 12 2022
-
from sympy import Matrix, prime
def A356491(n): return Matrix(n,n,[prime(abs(i-j)+1) for i in range(n) for j in range(n)]).per() if n else 1 # Chai Wah Wu, Aug 12 2022
A330087
Permanent of a square matrix M(n) whose general element M_{i,j} is defined by i*prime(j).
Original entry on oeis.org
1, 2, 24, 1080, 120960, 33264000, 15567552000, 12967770816000, 15768809312256000, 29377291748732928000, 85194146071325491200000, 319563241913541917491200000, 1702632952915351336393113600000, 11797543730750469409867884134400000, 99429698562764956186366527484723200000
Offset: 0
For n = 1 the matrix M(1) is
2
with permanent a(1) = 2.
For n = 2 the matrix M(2) is
2, 3
4, 6
with permanent a(2) = 24.
For n = 3 the matrix M(3) is
2, 3, 5
4, 6, 10
6, 9, 15
with permanent a(3) = 1080.
-
with(LinearAlgebra):
a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> i*ithprime(j)))):
seq(a(n), n=0..14); # Alois P. Heinz, Dec 04 2019
-
M[i_, j_, n_] := i*Prime[j]; a[n_] := If[n==0,1,Permanent[Table[M[i, j, n], {i, n}, {j, n}]]]; Array[a, 14, 0]
-
a(n) = matpermanent(matrix(n, n, i, j, i*prime(j))); \\ Michel Marcus, Dec 04 2019
Showing 1-3 of 3 results.
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