A164468 - OEIS

%I #19 Aug 12 2023 16:43:19

%S 13,20,30,45,67,99,146,215,316,464,681,999,1465,2148,3149,4616,6766,

%T 9917,14535,21303,31222,45759,67064,98288,144049,211115,309405,453456,

%U 664573,973980,1427438,2092013,3065995,4493435,6585450,9651447,14144884

%N Number of binary strings of length n with no substrings equal to 0001, 0100, or 1110.

%H R. H. Hardin, <a href="/A164468/b164468.txt">Table of n, a(n) for n = 4..500</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-1).

%F G.f.: -x^4*(-13+6*x-3*x^2+8*x^3) / ( (x-1)*(x^3+x-1) ). - _R. J. Mathar_, Jan 19 2011

%F a(n) = a(n-1) + a(n-3) + 2 for n>6. - _Greg Dresden_, Feb 09 2020

%t LinearRecurrence[{2,-1,1,-1},{13,20,30,45},40] (* _Harvey P. Dale_, Aug 12 2023 *)

%K nonn

%O 4,1

%A _R. H. Hardin_, Aug 14 2009