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%I #15 Nov 17 2022 19:24:40
%S 13,21,32,48,70,101,144,204,287,402,561,781,1085,1505,2085,2886,3992,
%T 5519,7627,10537,14554,20099,27753,38318,52901,73030,100814,139164,
%U 192098,265162,366011,505211,697346,962546,1328596,1833847,2531234
%N Number of binary strings of length n with no substrings equal to 0001 0010 or 1101.
%H R. H. Hardin, <a href="/A164452/b164452.txt">Table of n, a(n) for n = 4..500</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1,-2,1).
%F G.f.: -x^4*(13-18*x+8*x^2+2*x^3-12*x^4+8*x^5) / ( (x^4+x-1)*(x-1)^2 ). - _R. J. Mathar_, Jan 19 2011
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 2*a(n-5) + a(n-6). - _Wesley Ivan Hurt_, Nov 17 2022
%t CoefficientList[Series[(13 - 18*x + 8*x^2 + 2*x^3 - 12*x^4 + 8*x^5)/((1 - x - x^4)*(x - 1)^2), {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Nov 17 2022 *)
%K nonn,easy
%O 4,1
%A _R. H. Hardin_, Aug 14 2009
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