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