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 A318173 The determinant of an n X n Toeplitz matrix M(n) whose first row consists of successive prime numbers prime(1), ..., prime(n) and whose first column consists of prime(1), prime(n + 1), ..., prime(2*n - 1). 13
 2, -11, 158, -6513, 202790, -12710761, 578257422, -45608219247, 8774909485920, -579515898830751, 115918088707226940, -16737522590543449641, 1282860173728469083872, -189053227741259934603831, 55171097827950314187327460, -16235234399834578732807710581 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The trace of the matrix M(n) is A005843(n). The sum of the first row of the matrix M(n) is A007504(n). The permanent of the matrix M(n) is A306457(n). For n > 1, the subdiagonal sum of the matrix M(n) is A306192(n). 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 Cf. A005843, A000040, A007504, A306457, A306192. Sequence in context: A058154 A275923 A288560 * A349639 A067968 A295269 Adjacent sequences: A318170 A318171 A318172 * A318174 A318175 A318176 KEYWORD sign AUTHOR Stefano Spezia, Aug 20 2018 STATUS approved

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Last modified September 11 23:02 EDT 2024. Contains 375842 sequences. (Running on oeis4.)