A320429 The length of the shortest prefix of the Thue-Morse word decomposable to not less than n palindromes.

1, 2, 6, 10, 26, 90, 154, 410, 1434, 2458, 6554, 22938, 39322, 104858, 367002, 629146, 1677722, 5872026, 10066330, 26843546, 93952410, 161061274, 429496730, 1503238554, 2576980378, 6871947674, 24051816858, 41231686042, 109951162778, 384829069722, 659706976666, 1759218604442, 6157265115546

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

A. E. Frid, Prefix palindromic length of the Thue-Morse word, arXiv:1906.09392 [cs.DM] (2019).

Index entries for linear recurrences with constant coefficients, signature (1,0,16,-16).

Formula

a(n+3) = 16*a(n) - 6.

From Stefano Spezia, Apr 17 2023: (Start)

G.f.: x*(1 + x + 4*x^2 - 12*x^3)/((1 - x)*(1 - 16*x^3)).

a(n) = a(n-1) + 16*a(n-3) - 16*a(n-4) for n > 4. (End)

Mathematica

LinearRecurrence[{1, 0, 16, -16}, {1, 2, 6, 10}, 35] (* Paolo Xausa, Jul 09 2026 *)

Prog

(PARI) a(n)=if(n<=3, [1, 2, 6][n], 16*a(n-3)-6); \\ Joerg Arndt, Aug 27 2019

Crossrefs

Cf. Thue-Morse word A010060. Indices of new values of A307319.

Sequence in context: A162581 A061547 A218791 * A319014 A190034 A119459

Adjacent sequences: A320426 A320427 A320428 * A320430 A320431 A320432

Keyword

easy,nonn,changed

Author

Anna Frid, Aug 27 2019

Status

approved