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%I #24 Mar 26 2024 10:34:29
%S 0,0,1,9,65,421,2569,15085,86241,483429,2669305,14564061,78699089,
%T 421880725,2246459881,11894065549,62665617345,328756309701,
%U 1718275598809,8951067087165,46492068009521,240846026714869,1244719810538185,6419100507215341
%N The number of quinary strings of length n containing 00.
%H Michael De Vlieger, <a href="/A351530/b351530.txt">Table of n, a(n) for n = 0..1430</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-16,-20).
%F G.f.: x^2 / ( (5*x-1)*(4*x^2+4*x-1) ).
%F a(n) = 5^n - A086347(n).
%F a(n) = 9*a(n-1) - 16*a(n-2) - 20*a(n-3). - _Wesley Ivan Hurt_, Jun 22 2022
%t CoefficientList[Series[x^2/((5*x - 1)*(4*x^2 + 4*x - 1)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Jun 22 2022 *)
%t LinearRecurrence[{9,-16,-20},{0,0,1},30] (* _Harvey P. Dale_, Mar 26 2024 *)
%Y Cf. A008466 (2-ary), A186244 (3-ary), A351529 (4-ary), A086347 (not containing 00).
%K nonn,easy
%O 0,4
%A _R. J. Mathar_, Feb 13 2022
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