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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
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
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.)