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Number of binary strings of length n with no substrings equal to 0001, 1010, or 1100.
1

%I #20 Mar 31 2024 01:56:39

%S 1,2,4,8,13,20,30,44,64,93,135,196,285,415,605,883,1290,1886,2759,

%T 4038,5912,8658,12682,18579,27221,39886,58447,85649,125515,183941,

%U 269568,395060,578977,848520,1243554,1822504,2670996,3914521,5736995,8407960,12322449

%N Number of binary strings of length n with no substrings equal to 0001, 1010, or 1100.

%H Alois P. Heinz, <a href="/A164487/b164487.txt">Table of n, a(n) for n = 0..2000</a> (first 500 terms from R. H. Hardin)

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-2,1).

%F G.f.: (x^6+x^4-x^2+x-1)/((x^3+x-1)*(x-1)^2). - _R. J. Mathar_, Jan 19 2011

%t LinearRecurrence[{3,-3,2,-2,1},{1,2,4,8,13,20,30},50] (* _Harvey P. Dale_, Aug 14 2023 *)

%K nonn,easy

%O 0,2

%A _R. H. Hardin_, Aug 14 2009

%E Edited by _Alois P. Heinz_, Oct 27 2017