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a(n) is the number of binary strings of length n not containing the substrings 0000, 0001, 0011, 0111, 1111.
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%I #40 Jun 24 2024 10:51:10

%S 1,2,4,8,11,18,28,40,64,96,144,224,336,512,784,1184,1808,2752,4176,

%T 6368,9680,14720,22416,34080,51856,78912,120016,182624,277840,422656,

%U 643088,978336,1488400,2264512,3445072,5241312,7974096,12131456,18456720,28079648

%N a(n) is the number of binary strings of length n not containing the substrings 0000, 0001, 0011, 0111, 1111.

%H Paolo Xausa, <a href="/A373080/b373080.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,2).

%F a(n) = a(n-2) + 2*a(n-3) for n >= 7.

%F G.f.: -(x+1)^2*(x^2+1)^2/(2*x^3+x^2-1). - _Alois P. Heinz_, Jun 03 2024

%t LinearRecurrence[{0, 1, 2}, {1, 2, 4, 8, 11, 18, 28}, 50] (* _Paolo Xausa_, Jun 24 2024 *)

%Y Cf. A052947, A164395, A164408, A368430.

%K nonn,easy

%O 0,2

%A _Miquel A. Fiol_, Jun 03 2024