A186026 Hankel transform of Thue-Morse related sequence A106400.

1, 1, -2, 4, 8, -16, -32, -64, 128, -256, -1536, -3072, 2048, 4096, 8192, -16384, 32768, -65536, -393216, -2359296, 14155776, 28311552, -94371840, 62914560, 8388608, 16777216, -570425344, -1140850688, -134217728, 268435456, -8053063680, 16106127360, 2147483648, -4294967296, 111669149696, 670014898176, 927712935936, 5566277615616

Offset

0,3

Links

Table of n, a(n) for n=0..37.

J.-P. Allouche, J. Peyrière, Z.-X. Wen and Z.-Y. Wen, Hankel determinants of the Thue-Morse sequence, Ann. Inst. Fourier, Grenoble, 48 (1998), pp. 1-27.

Yann Bugeaud and Guo-Niu Han, A combinatorial proof of the non-vanishing of Hankel determinants of the Thue-Morse sequence, Electronic Journal of Combinatorics 21(3) (2014), #P3.26.

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

Guo-Niu Han and Wen Wu, Evaluations of the Hankel determinants of a Thue-Morse-like sequence, International Journal of Number Theory, World Scientific Publishing, 2015, 11 (6), 10.1142/S1793042115500815, hal-01278054.

Formula

a(n) = Product{k=0..n} (A186027(k)/A186028(k))^(n-k).

Prog

(PARI) a(n) = matdet(matrix(n, n, i, j, (-1)^hammingweight(i+j-2))); \\ Michel Marcus, Apr 13 2020

Crossrefs

Cf. A106400, A186027, A186028.

Sequence in context: A180211 A275075 A275063 * A367653 A023423 A210544

Adjacent sequences: A186023 A186024 A186025 * A186027 A186028 A186029

Keyword

sign

Author

Paul Barry, Feb 10 2011

Extensions

a(0)=1 inserted by Michel Marcus, May 16 2020

Status

approved