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%I #13 Jun 27 2021 12:38:12
%S 2,8,56,1472,615872,66741913472,481633806031213129472,
%T 14977615127386591957251601320841928924672,
%U 8683854397629333456697983324568080952156333564253951567157061992396002450127872
%N Total number of nodes of the binary decision diagrams (BDDs) for all Boolean functions of n variables.
%D D. E. Knuth, The Art of Computer Programming, Vol. 4A, Addison-Wesley, 2011, Section 7.1.4.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Binary_decision_diagram">Binary decision diagram</a>
%F a(n) = 2*(2^2^n-1) + Sum_{k=0..n-1} (2^2^(n-k)-2^2^(n-k-1))*(2^2^n-(2^2^(n-k)-1)^2^k).
%F a(n) < 2^2^n*A327461(n) for n >= 1.
%t a[n_]:=2(2^2^n-1)+Sum[(2^2^(n-k)-2^2^(n-k-1))*(2^2^n-(2^2^(n-k)-1)^2^k),{k,0,n-1}]; Array[a,9,0] (* _Stefano Spezia_, Jun 26 2021 *)
%Y Cf. A327461, A345678.
%K nonn
%O 0,1
%A _Pontus von Brömssen_, Jun 22 2021
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