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A334910
Hankel transform of the ruler function A001511.
1
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
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
KEYWORD
sign,look
AUTHOR
Michel Marcus, May 16 2020
STATUS
approved