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 A382359 #13 Sep 03 2025 15:15:06 %S A382359 2,128,17496,4194304,1562500000,835884417024,607687873272704, %T A382359 576460752303423488,691636079448571949568,1024000000000000000000000, %U A382359 1833841138186726138360895488,3907429033741066770846918377472,9769232732262334599652925506494464 %N A382359 Number of labeled deterministic finite automata with n states and two letters. %C A382359 The first term in the product represents the n-choices for the starting state. The second term represents the subset of states to designate as accepting. The third term is the number of transition functions with an alphabet of length two. %F A382359 a(n) = n * 2^n * n^(2*n). %F A382359 a(n) = n * A155957(n). %F A382359 a(n) = A036289(n) * A062206(n). %e A382359 For n = 1, we have two choices (a(1)=2), either the node is an accept state or not. We have no choice but to send both letters of the alphabet to itself, and only one choice for the start state. Therefore 1*2*1 = 2. %e A382359 For n = 2, we have 2 choices for starting, 4 choices for which states are accepting, and 2^4 choices for transition functions. So a(2) = 2*4*16 = 128. %t A382359 a[n_]:= n * 2^n * n^(2*n); Array[a,13] (* _Stefano Spezia_, Sep 03 2025 *) %Y A382359 Cf. A036289, A062206, A155957. %K A382359 nonn,changed %O A382359 1,1 %A A382359 _Anand Jain_, Mar 22 2025