A000615 Threshold functions of exactly n variables. (Formerly M0379 N0142 N0747)

2, 2, 8, 72, 1536, 86080, 14487040, 8274797440, 17494930604032

Offset

0,1

References

S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 4.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence in two entries, N0142 and N0747).

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

Links

Table of n, a(n) for n=0..8.

Goto, Eiichi, and Hidetosi Takahasi, Some Theorems Useful in Threshold Logic for Enumerating Boolean Functions, in Proceedings International Federation for Information Processing (IFIP) Congress, 1962, pp. 747-752. [Annotated scans of certain pages]

Alastair D. King, Comments on A002080 and related sequences based on threshold functions, Mar 17 2023.

S. Muroga, I. Toda and M. Kondo, Majority decision functions of up to six variables, Math. Comp., 16 (1962), 459-472.

S. Muroga, I. Toda and M. Kondo, Majority decision functions of up to six variables, Math. Comp., 16 (1962), 459-472. [Annotated partially scanned copy]

S. Muroga, T. Tsuboi and C. R. Baugh, Enumeration of threshold functions of eight variables, IEEE Trans. Computers, 19 (1970), 818-825.

S. Muroga, T. Tsuboi and C. R. Baugh, Enumeration of threshold functions of eight variables, IEEE Trans. Computers, 19 (1970), 818-825. [Annotated scanned copy]

Index entries for sequences related to Boolean functions

Formula

A000609(n) = Sum_{k=0..n} a(k)*binomial(n,k). - Alastair D. King, Mar 17, 2023.

Crossrefs

Cf. A000609.

Sequence in context: A009616 A005615 A048617 * A297010 A012413 A012659

Adjacent sequences: A000612 A000613 A000614 * A000616 A000617 A000618

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

Entry revised by N. J. A. Sloane, Jun 11 2012

Status

approved