A384482 Number of functions f(x) = b*x+c with nonnegative integer coefficients and a shortest addition-composition chain of length n, starting with 1 and x.
2, 3, 7, 20, 75, 412, 3200, 34167, 507344
Offset: 0
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The smallest n for which a(n) < A230697(n) is n = 31. The length of a shortest addition-multiplication chain for 31 is A230697(31) = 6, but there are addition-multiplication-composition chains of length 5, for example (1, x,) 2*x, 2*x+1, 4*x+3, 7, 31. (4*x+3 is the composition of 2*x+1 with itself; 7 and 31 are the compositions of 4*x+3 with 1 and 7, respectively.)
a(0) = 2 because 1 and x are considered to have chains of length 0. a(1) = 4 because the 4 polynomials 2, x+1, 2*x, and x^2 have chains of length 1. a(2) = 14 because the 14 polynomials 3, 4, x+2, 2*x+1, 2*x+2, 3*x, 4*x, x^2+1, x^2+x, x^2+2*x+1, 2*x^2, 4*x^2, x^3, and x^4 have chains of length 2.
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