A006845 State assignments for n-state machine.

0, 1, 3, 3, 140, 420, 840, 840, 10810800, 75675600, 454053600, 2270268000, 9081072000, 27243216000, 54486432000, 54486432000, 52401161274029568000, 786017419110443520000, 11004243867546209280000, 143055170278100720640000

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

After the initial 0, this sequence is formed by taking in turn the last 2^(n-1) elements of row n in the irregular triangle A133709. - Sean A. Irvine, Aug 14 2017

References

• F. J. Hill and G. R. Peterson, Introduction to Switching Theory and Logical Design. Wiley, NY, 3rd ed., 1981, p. 308.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• D. Fielder, Letters to N. J. A. Sloane (with attachment), 1991

Crossrefs

Cf. A007041, A133709.

Programs

Mathematica

T[m_, l_] := T[m, l] = If[l == 1, 1, Sum[(-1)^i Binomial[l, i]* Binomial[2^(l - i) + m - 2, m], {i, 0, l - 1}] - Sum[StirlingS2[l, i]* T[m, i], {i, 1, l - 1}]];
Join[{{0}}, Table[Table[T[m, l], {l, 2^m - 2^(m-1), 2^m - 1}], {m, 1, 5}]] // Flatten (* Jean-François Alcover, Apr 03 2020 *)

Extensions

a(9) corrected and more terms from Sean A. Irvine, Aug 14 2017