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%I #21 Mar 09 2021 20:35:14
%S 0,0,0,0,4,15,41,98,218,465,967,1980,4016,8099,16277,32646,65398,
%T 130917,261971,524096,1048364,2096919,4194049,8388330,16776914,
%U 33554105,67108511,134217348,268435048,536870475,1073741357,2147483150,4294966766,8589934029
%N Expansion of e.g.f. (exp(x)-1)*(exp(x) - x^2/2 - x - 1).
%C a(n) is the number of binary strings of length n that contain at least three 0's but not all digits are 0.
%C a(n) is also the number of proper subsets with at least three elements of an n-element set.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2).
%F a(n) = 2^n - Sum_{i={0,1,2,n}} binomial(n,i).
%F G.f.: x^4*(2*x^2-5*x+4)/((2*x-1)*(x-1)^3). - _Alois P. Heinz_, Mar 09 2021
%e a(6) = 41 since the strings are the 20 permutations of 000111, the 15 permutations of 000011, and the 6 permutations of 000001.
%Y Cf. A000079, A000247, A002662.
%K nonn,easy
%O 0,5
%A _Enrique Navarrete_, Mar 08 2021
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