This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384382 #8 Jun 09 2025 10:38:43 %S A384382 2,4,14,62,350,2517,22918,259325 %N A384382 Number of polynomials with a shortest addition-multiplication chain of length n, starting with 1 and x. %C A384382 An addition-multiplication chain for the polynomial p(x) is a finite sequence of polynomials, starting with 1, x and ending with p(x), in which each element except 1 and x equals q(x)+r(x) or q(x)*r(x) for two preceding, not necessarily distinct, elements q(x) and r(x) in the chain. The length of the chain is the number of elements in the chain, excluding 1 and x. %e A384382 a(0) = 2 because 1 and x are considered to have chains of length 0. %e A384382 a(1) = 4 because the 4 polynomials 2, x+1, 2*x, and x^2 have chains of length 1. %e A384382 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. %Y A384382 Cf. A382928, A383002, A383331 (addition only), A384383 (addition, multiplication, and composition), A384482 (addition and composition). %K A384382 nonn,more %O A384382 0,1 %A A384382 _Pontus von Brömssen_, Jun 01 2025