A006845 State assignments for n-state machine. (Formerly M2295)

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

Offset

1,3

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

Table of n, a(n) for n=1..20.

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

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 *)

Crossrefs

Cf. A007041, A133709.

Sequence in context: A173797 A173127 A230646 * A071536 A094755 A152418

Adjacent sequences: A006842 A006843 A006844 * A006846 A006847 A006848

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved