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%I #9 Mar 07 2021 19:49:23
%S 1,1,1,1,3,11,31,71,211,883,3571,12211,35641,91521,212213,453181,
%T 904541,1706461,3069181,5298493,8827591,14256271,22398531,34339691,
%U 51504223,75735551,109389151,155440351,217608301,300497653,409759561,552273681,736352921,971972761
%N a(n) = 70*binomial(n,8) + 2*binomial(n,4) + 1.
%C a(n) is the number of ternary strings of length n that contain either none or four 0's and either none or four 1's.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F E.g.f.: exp(x)*(1 + x^4/24)^2.
%F O.g.f.:(1 - 8*x + 28*x^2 - 56*x^3 + 72*x^4 - 64*x^5 + 40*x^6 - 16*x^7 + 73*x^8)/(1 - x)^9. - _Stefano Spezia_, Feb 19 2021
%e a(9)=883 since the strings are the 630 permutations of 000011112, the 126 permutations of 000022222, the 126 permutations of 111122222, and 222222222.
%Y Cf. A341703, A341704.
%K nonn,easy
%O 0,5
%A _Enrique Navarrete_, Feb 17 2021
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