A334910 Hankel transform of the ruler function A001511.

1, 1, -3, -1, 21, 1, -3, -9, 945, 9, -3, -1, 21, 9, -243, -3969, 1845585, 3969, -243, -9, 21, 1, -3, -9, 945, 81, -243, -729, 137781, 321489, -47258883, -3544416225, 6922244887425, 3544416225, -47258883, -321489, 137781, 729, -243, -81, 945, 9, -3, -1, 21, 9

Offset

0,3

Comments

All terms are odd. See Coons and Han.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Michael Coons, On the rational approximation of the sum of the reciprocals of the Fermat numbers, arXiv:1112.5072 [math.NT], 2011. See Hankel determinants and the ruler function pp. 2 ff.

Guo-Niu Han, Hankel determinant calculus for the Thue-Morse and related sequences, Journal of Number Theory, Volume 147, February 2015, Pages 374-395. See p. 377.

Maple

a:= n-> LinearAlgebra[Determinant](Matrix(n,
        (i, j)-> 1+padic[ordp](i+j-1, 2))):
seq(a(n), n=0..45);  # Alois P. Heinz, May 16 2020

Mathematica

a[0] = 1; a[n_] := Det @ Table[1 + IntegerExponent[i+j-1, 2], {i, 1, n}, {j, 1, n}]; Array[a, 46, 0] (* Amiram Eldar, May 16 2020 *)

Prog

(PARI) a(n) = matdet(matrix(n, n, i, j, valuation(i+j-1, 2)+1));

Crossrefs

Cf. A001511.

Sequence in context: A030042 A045496 A024432 * A016531 A221365 A144279

Adjacent sequences: A334907 A334908 A334909 * A334911 A334912 A334913

Keyword

sign,look

Author

Michel Marcus, May 16 2020

Status

approved