A164414 - OEIS

%I #19 Jun 11 2021 00:26:29

%S 1,2,4,8,13,22,37,63,107,181,307,521,883,1497,2539,4305,7299,12377,

%T 20987,35585,60339,102313,173483,294161,498787,845753,1434075,2431649,

%U 4123155,6991305,11854603,20100913,34083523,57792729,97994555,166161601,281747059

%N Number of binary strings of length n with no substrings equal to 0000, 0001, or 1010.

%H Alois P. Heinz, <a href="/A164414/b164414.txt">Table of n, a(n) for n = 0..2000</a> (terms n=4..500 from R. H. Hardin)

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

%F From _R. J. Mathar_, Nov 30 2011: (Start)

%F a(n) = 13*A077949(n-4) + 9*A077949(n-5) + 15*A077949(n-6).

%F G.f.: (x^6-x^5-x^4-2*x^3-2*x^2-x-1)/(2*x^3+x-1).

%F (End)

%Y Cf. A077949.

%K easy,nonn

%O 0,2

%A _R. H. Hardin_, Aug 14 2009

%E a(0)-a(3) from _Alois P. Heinz_, Jun 10 2021