OFFSET
0,5
COMMENTS
a(n) is the number of binary strings of length n that contain at least three 0's but not all digits are 0.
a(n) is also the number of proper subsets with at least three elements of an n-element set.
LINKS
Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).
FORMULA
a(n) = 2^n - Sum_{i={0,1,2,n}} binomial(n,i).
G.f.: x^4*(2*x^2-5*x+4)/((2*x-1)*(x-1)^3). - Alois P. Heinz, Mar 09 2021
EXAMPLE
a(6) = 41 since the strings are the 20 permutations of 000111, the 15 permutations of 000011, and the 6 permutations of 000001.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Enrique Navarrete, Mar 08 2021
STATUS
approved