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Number of binary strings of length n with no substrings equal to 0000 or 0110.
2

%I #21 Jul 25 2021 13:55:04

%S 1,2,4,8,14,25,44,79,141,253,452,809,1446,2587,4626,8275,14799,26470,

%T 47341,84673,151439,270857,484436,866436,1549652,2771618,4957145,

%U 8866056,15857289,28361399,50725485,90724558,162264477,290216490,519063741,928366188

%N Number of binary strings of length n with no substrings equal to 0000 or 0110.

%H Alois P. Heinz, <a href="/A164390/b164390.txt">Table of n, a(n) for n = 0..2000</a> (first 500 terms from R. H. Hardin)

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,1,0,1).

%F G.f.: -(x^5+x^4+2*x^3+x^2+x+1)/(x^6+x^4+x^2+x-1). - _R. J. Mathar_, Nov 28 2011

%t LinearRecurrence[{1,1,0,1,0,1}, {14, 25, 44, 79, 141, 253}, 50] (* _G. C. Greubel_, Sep 18 2017 *)

%K nonn,easy

%O 0,2

%A _R. H. Hardin_, Aug 14 2009

%E Edited by _Alois P. Heinz_, Oct 12 2017