login
The length of the shortest prefix of the Thue-Morse word decomposable to not less than n palindromes.
0

%I #22 Apr 18 2023 08:30:14

%S 1,2,6,10,26,90,154,410,1434,2458,6554,22938,39322,104858,367002,

%T 629146,1677722,5872026,10066330,26843546,93952410,161061274,

%U 429496730,1503238554,2576980378,6871947674,24051816858,41231686042,109951162778,384829069722,659706976666,1759218604442,6157265115546

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

%H A. E. Frid, <a href="https://arxiv.org/abs/1906.09392">Prefix palindromic length of the Thue-Morse word</a>, arXiv:1906.09392 [cs.DM] (2019).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,16,-16).

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

%F From _Stefano Spezia_, Apr 17 2023: (Start)

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

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

%o (PARI) a(n)=if(n<=3,[1, 2, 6][n],16*a(n-3)-6); \\ _Joerg Arndt_, Aug 27 2019

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

%K easy,nonn

%O 1,2

%A _Anna Frid_, Aug 27 2019