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Number of binary strings of length n with no substrings equal to 0001 0101 or 1110.
1

%I #16 Mar 31 2024 01:55:53

%S 13,20,30,44,63,90,128,180,253,356,498,696,975,1362,1900,2656,3709,

%T 5172,7222,10084,14063,19626,27400,38220,53325,74436,103850,144880,

%U 202207,282146,393620,549304,766509,1069396,1492238,2082332,2905311,4053882

%N Number of binary strings of length n with no substrings equal to 0001 0101 or 1110.

%H R. H. Hardin, <a href="/A164475/b164475.txt">Table of n, a(n) for n=4..500</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-1,-1).

%F G.f.: -x^4*(-13-7*x-10*x^2+12*x^3+8*x^4) / ( (x-1)*(x^4+2*x^3-1) ). - _R. J. Mathar_, Jan 19 2011

%t LinearRecurrence[{1,0,2,-1,-1},{13,20,30,44,63},50] (* _Harvey P. Dale_, Jun 24 2021 *)

%K nonn,easy

%O 4,1

%A _R. H. Hardin_, Aug 14 2009