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%I #37 Sep 08 2022 08:44:50
%S 4,12,40,144,544,2112,8320,33024,131584,525312,2099200,8392704,
%T 33562624,134234112,536903680,2147549184,8590065664,34360000512,
%U 137439477760,549756862464,2199025352704,8796097216512,35184380477440,140737505132544,562949986975744
%N Number of types of Boolean functions of n variables under a certain group.
%H Harvey P. Dale, <a href="/A028403/b028403.txt">Table of n, a(n) for n = 1..1000</a>
%H I. Strazdins, <a href="http://dx.doi.org/10.1023/A:1005769927571">Universal affine classification of Boolean functions</a>, Acta Applic. Math. 46 (1997), 147-167.
%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-8).
%F a(n) = (2^(n-1) + 1)*2^n = 2*A007582(n-1). - _Ralf Stephan_, Mar 24 2004
%F a(n) = A000079(n) * (A000079(n-1) + 1) = (A000051(n) - 1) * A000051(n-1) = A000079(n) * A000051(n-1) = (A000051(n) - 1) * (A000079(n-1) + 1) = 2^n * (2^(n-1) + 1). a(n+1) = A000079(n+1) * (A000079(n) + 1) = (A000051(n+1) - 1) * A000051(n) = A000079(n+1) * A000051(n) = (A000051(n+1) - 1) * (A000079(n) + 1) = 2^(n+1) * (2^n + 1). a(n) = A081294(n) + A000079(n) = A004171(n-1) + A000079(n) = 2^(2n-1) + 2^n. - _Jaroslav Krizek_, Jul 27 2009
%F From _Colin Barker_, Sep 30 2014: (Start)
%F a(n) = 6*a(n-1) - 8*a(n-2).
%F G.f.: 4*x*(1 - 3*x)/((1-2*x)*(1-4*x)). (End)
%F E.g.f.: (1/2)*(exp(2*x) -1)*(exp(2*x) + 3). - _G. C. Greubel_, Jul 07 2021
%t Join[{4},Table[FromDigits[Join[{1},PadRight[{},n-2,0],{1},PadRight[ {},n,0]],2],{n,2,30}]] (* _Harvey P. Dale_, Jan 24 2021 *)
%o (PARI) Vec(4*x*(1-3*x)/((1-2*x)*(1-4*x)) + O(x^100)) \\ _Colin Barker_, Sep 30 2014
%o (Magma) [2^(2*n-1) +2^n: n in [1..30]]; // _G. C. Greubel_, Jul 07 2021
%o (Sage) [2^(2*n-1) +2^n for n in (1..30)] # _G. C. Greubel_, Jul 07 2021
%Y Cf. A000051, A000079, A004171, A007582, A081294.
%Y This sequence in base 2 is A163450. - _Jaroslav Krizek_, Jul 27 2009
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Feb 24 2000
%E More terms from _Colin Barker_, Sep 30 2014
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