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 A186520 #11 Aug 21 2022 22:26:58 %S A186520 1,1,1,1,1,2,4,1,1,2,4,3,5,10,2,1,1,2,4,3,5,10,2,4,7,12,2,16,47,6,22, %T A186520 1,1,2,4,3,5,10,10,4,6,12,2,18,2,4,10,5,7,17,2,19,55,6,28,22,49,120,8, %U A186520 12 %N A186520 Number of evaluation schemes for x^n achieving the minimal number of multiplications, and with the maximal number of squarings among the multiplications. %e A186520 For n=7, we can evaluate x^7 using only 4 operations in 6 ways: %e A186520 x^2 = x * x ; x^3 = x * x^2 ; x^4 = x * x^3 ; x^7 = x^3 * x^4 (1 squaring) %e A186520 x^2 = x * x ; x^3 = x * x^2 ; x^4 = x^2 * x^2 ; x^7 = x^3 * x^4 (2 squarings) %e A186520 x^2 = x * x ; x^3 = x * x^2 ; x^5 = x^2 * x^3 ; x^7 = x^2 * x^5 (1 squaring) %e A186520 x^2 = x * x ; x^3 = x * x^2 ; x^6 = x^3 * x^3 ; x^7 = x * x^6 (2 squarings) %e A186520 x^2 = x * x ; x^4 = x^2 * x^2 ; x^5 = x * x^4 ; x^7 = x^2 * x^5 (2 squarings) %e A186520 x^2 = x * x ; x^4 = x^2 * x^2 ; x^6 = x^2 * x^4 ; x^7 = x * x^6 (2 squarings) %e A186520 The maximal number of squarings in these evaluation schemes is 2, and it is achieved by a(7) = 4 schemes. %Y A186520 Cf A003313, A186435, A186437. %K A186520 nonn %O A186520 1,6 %A A186520 Laurent Thévenoux and _Christophe Mouilleron_, Feb 23 2011