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 A364233 Triangle read by rows: T(n, k) is the number of n X n symmetric Toeplitz matrices of rank k using all the first n prime numbers integers. 1
 1, 0, 2, 0, 0, 6, 0, 0, 0, 24, 0, 0, 0, 0, 120, 0, 0, 0, 0, 2, 718, 0, 0, 0, 0, 0, 4, 5036, 0, 0, 0, 0, 0, 1, 3, 40316, 0, 0, 0, 0, 0, 0, 0, 18, 362862, 0, 0, 0, 0, 0, 0, 0, 0, 14, 3628786, 0, 0, 0, 0, 0, 0, 0, 0, 0, 99, 39916701, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 78, 479001517 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..78. Wikipedia, Toeplitz Matrix EXAMPLE The triangle begins: 1; 0, 2; 0, 0, 6; 0, 0, 0, 24; 0, 0, 0, 0, 120; 0, 0, 0, 0, 2, 718; 0, 0, 0, 0, 0, 4, 5036; ... MATHEMATICA T[n_, k_]:= Count[Table[MatrixRank[ToeplitzMatrix[Part[Permutations[Prime[Range[n]]], i]]], {i, n!}], k]; Table[T[n, k], {n, 8}, {k, n}]//Flatten PROG (PARI) MkMat(v)={matrix(#v, #v, i, j, v[1+abs(i-j)])} row(n)={my(f=vector(n)); forperm(vector(n, i, prime(i)), v, f[matrank(MkMat(v))]++); f} \\ Andrew Howroyd, Dec 31 2023 CROSSREFS Cf. A000142 (row sums), A348891 (minimal nonzero absolute value determinant), A350955 (minimal determinant), A350956 (maximal determinant), A351021 (minimal permanent), A351022 (maximal permanent), A364234 (right diagonal). Sequence in context: A132710 A106512 A181229 * A364230 A259857 A364790 Adjacent sequences: A364230 A364231 A364232 * A364234 A364235 A364236 KEYWORD nonn,tabl AUTHOR Stefano Spezia, Jul 14 2023 EXTENSIONS Terms a(46) and beyond from Andrew Howroyd, Dec 31 2023 STATUS approved

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Last modified July 25 08:34 EDT 2024. Contains 374586 sequences. (Running on oeis4.)