A000838 - OEIS

%I M3629 N1474 #42 Feb 02 2022 04:51:27

%S 4,28,2272,67170304,144115192236605440,

%T 1329227995784915891062320757838184448,

%U 226156424291633194186662080095093570363541849729447858357132587076662853632

%N Number of n-input 2-output switching networks under action of complementing group on the inputs and outputs.

%D M. A. Harrison, On the number of classes of switching networks, J. Franklin Instit., 276 (1963), 313-327.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H <a href="/index/Sw#switching">Index entries for sequences related to switching networks</a>

%F a(n) = 2^(2^(n+1) - 2 - n) + 2^(2^n) - 2^(2^n-n). - _Sean A. Irvine_, Jul 14 2011

%F G.f.: A(x) = G(0) - 1; G(k) = 1 + (8*2^k - 8 + 8^2^k*x*G(k+1))/2^(2^k+1). - _Sergei N. Gladkovskii_, Dec 02 2011 [edited by _Michael Somos_, Sep 07 2013]

%e G.f. = 4*x + 28*x^2 + 2272*x^3 + 67170304*x^4 + 144115192236605440*x^5 + ...

%t a[ n_] := If[ n < 1, 0, 2^(2^(n + 1) - 2 - n) + 2^2^n - 2^(2^n - n)]; (* _Michael Somos_, Aug 17 2015 *)

%o (PARI) {a(n) = if( n<1, 0, 2^(2^(n+1) - 2 - n) + 2^(2^n) - 2^(2^n - n))}; /* _Michael Somos_, Sep 07 2013 */

%Y Cf. A000133, A000839.

%K easy,nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Vladeta Jovovic_, Feb 26 2000