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 A186435 #9 Mar 31 2012 10:25:33 %S A186435 1,1,1,1,2,2,6,1,3,4,19,3,10,16,4,1,2,7,37,6,31,48,4,4,14,24,5,26,152, %T A186435 12,80,1,2,4,51,12,39,100,20,8,23,90,4,81,14,8,242,5,12,36,4,38,215, %U A186435 16,172,36,190,395,40,24 %N A186435 Number of evaluation schemes for x^n achieving the minimal number of multiplications. %e A186435 For n=7, we can evaluate x^7 using only 4 multiplications in 6 ways: %e A186435 x^2 = x * x ; x^3 = x * x^2 ; x^4 = x * x^3 ; x^7 = x^3 * x^4 %e A186435 x^2 = x * x ; x^3 = x * x^2 ; x^4 = x^2 * x^2 ; x^7 = x^3 * x^4 %e A186435 x^2 = x * x ; x^3 = x * x^2 ; x^5 = x^2 * x^3 ; x^7 = x^2 * x^5 %e A186435 x^2 = x * x ; x^3 = x * x^2 ; x^6 = x^3 * x^3 ; x^7 = x * x^6 %e A186435 x^2 = x * x ; x^4 = x^2 * x^2 ; x^5 = x * x^4 ; x^7 = x^2 * x^5 %e A186435 x^2 = x * x ; x^4 = x^2 * x^2 ; x^6 = x^2 * x^4 ; x^7 = x * x^6 %Y A186435 See A003313 for the minimal number of multiplications to evaluate x^n. %Y A186435 See A001190 for the total number of evaluation schemes for x^n (regardless of the number of effective multiplications). %Y A186435 A079300 gives the number of minimal chains (= sequences of powers of x) ending at x^n. This is actually a bit less than the number of evaluation schemes since two schemes may produce the same chain, like the first and second schemes in the example above, where the corresponding chain is (x^2, x^3, x^4, x^7). %K A186435 nonn %O A186435 1,5 %A A186435 Laurent Thevenoux and _Christophe Mouilleron_, Feb 23 2011