OFFSET
1,1
COMMENTS
LINKS
Robert Israel, Table of n, a(n) for n = 1..302
Wikipedia, Toeplitz Matrix
EXAMPLE
For n = 1 the matrix M(1) is
2
with determinant Det(M(1)) = 2.
For n = 2 the matrix M(2) is
2, 3
5, 2
with Det(M(2)) = -11.
For n = 3 the matrix M(3) is
2, 3, 5
7, 2, 3
11, 7, 2
with Det(M(3)) = 158.
MAPLE
f:= proc(n) uses LinearAlgebra;
Determinant(ToeplitzMatrix([seq(ithprime(i), i=2*n-1..n+1, -1), seq(ithprime(i), i=1..n)]))
end proc:
map(f, [$1..20]); # Robert Israel, Aug 30 2018
MATHEMATICA
p[i_]:=Prime[i]; a[n_]:=Det[ToeplitzMatrix[Join[{p[1]}, Array[p, n-1, {n+1, 2*n-1}]], Array[p, n]]]; Array[a, 20]
PROG
(PARI) tm(n) = {my(m = matrix(n, n, i, j, if (i==1, prime(j), if (j==1, prime(n+i-1))))); for (i=2, n, for (j=2, n, m[i, j] = m[i-1, j-1]; ); ); m; }
a(n) = matdet(tm(n)); \\ Michel Marcus, Mar 17 2019
CROSSREFS
KEYWORD
sign
AUTHOR
Stefano Spezia, Aug 20 2018
STATUS
approved