A028403 Number of types of Boolean functions of n variables under a certain group.

4, 12, 40, 144, 544, 2112, 8320, 33024, 131584, 525312, 2099200, 8392704, 33562624, 134234112, 536903680, 2147549184, 8590065664, 34360000512, 137439477760, 549756862464, 2199025352704, 8796097216512, 35184380477440, 140737505132544, 562949986975744

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.
• Index entries for sequences related to Boolean functions
• Index entries for linear recurrences with constant coefficients, signature (6,-8).

Crossrefs

Cf. A000051, A000079, A004171, A007582, A081294.

This sequence in base 2 is A163450. - Jaroslav Krizek, Jul 27 2009

Programs

Magma

[2^(2*n-1) +2^n: n in [1..30]]; // G. C. Greubel, Jul 07 2021

Mathematica

Join[{4},Table[FromDigits[Join[{1},PadRight[{},n-2,0],{1},PadRight[ {},n,0]],2],{n,2,30}]] (* Harvey P. Dale, Jan 24 2021 *)

PARI

Vec(4*x*(1-3*x)/((1-2*x)*(1-4*x)) + O(x^100)) \\ Colin Barker, Sep 30 2014

Sage

[2^(2*n-1) +2^n for n in (1..30)] # G. C. Greubel, Jul 07 2021

Formula

a(n) = (2^(n-1) + 1)*2^n = 2*A007582(n-1). - Ralf Stephan, Mar 24 2004

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

From Colin Barker, Sep 30 2014: (Start)

a(n) = 6*a(n-1) - 8*a(n-2).

G.f.: 4*x*(1 - 3*x)/((1-2*x)*(1-4*x)). (End)

E.g.f.: (1/2)*(exp(2*x) -1)*(exp(2*x) + 3). - G. C. Greubel, Jul 07 2021

Extensions

More terms from Vladeta Jovovic, Feb 24 2000

More terms from Colin Barker, Sep 30 2014