A005615 -id:A005615 - cp's OEIS frontend

A005743 Number of fanout-free Boolean functions of n variables using And, Or, Not and Majority gates.

2, 4, 14, 104, 1498, 32876, 950054, 33801424, 1426158002, 69573363284, 3851708875582, 238539414903224, 16338422029336970, 1226232142235080636, 100069553388048443990, 8822157207387535459616, 835558086134404986368866, 84609374709488540680125092

Offset: 0

N. J. A. Sloane

nonn

Kodandapani and Seth give incorrect a(7) = 33304122 (a consequence of former incorrect A005742(7)).

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

Andrew Howroyd, Table of n, a(n) for n = 0..200
K. L. Kodandapani and S. C. Seth, On combinational networks with restricted fan-out, IEEE Trans. Computers, 27 (1978), 309-318. (Annotated scanned copy)
Index entries for sequences related to Boolean functions

Cf. A005615, A005742.

a(n) = A005615(n) + A005742(n). - Sean A. Irvine, Jul 21 2016

Binomial transform of A005615. - Andrew Howroyd, Mar 29 2025

a(7) corrected and more terms from Sean A. Irvine, Jul 21 2016

a(0)=2 prepended and name clarified by Andrew Howroyd, Mar 29 2025

A005742 Number of degenerate fanout-free Boolean functions of n variables using And, Or, Not and Majority gates.

Original entry on oeis.org

2, 6, 32, 346, 6572, 176678, 6009040, 245551538, 11694413396, 635421164350, 38766848465336, 2622886302957962, 194847034853726140, 15763561489400425046, 1379408529039591621920, 129804134856816471241570, 13069901171127981930379940

Offset: 1

N. J. A. Sloane

nonn

Kodandapani and Seth paper gives incorrect a(7) = 5511738.

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

K. L. Kodandapani and S. C. Seth, On combinational networks with restricted fan-out, IEEE Trans. Computers, 27 (1978), 309-318. (Annotated scanned copy)
Index entries for sequences related to Boolean functions

Cf. A005615, A005743.

a(n) = Sum_{k=0..n-1} binomial(n, k) * A005615(k). - Sean A. Irvine, Jul 21 2016

a(7) corrected and more terms from Sean A. Irvine, Jul 21 2016

cp's OEIS Frontend

A005743 Number of fanout-free Boolean functions of n variables using And, Or, Not and Majority gates.

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