A005618 a(n) = 6*a(n-1) - 8, with a(0) = 4. (Formerly M3528)

4, 16, 88, 520, 3112, 18664, 111976, 671848, 4031080, 24186472, 145118824, 870712936, 5224277608, 31345665640, 188073993832, 1128443962984, 6770663777896, 40623982667368, 243743896004200, 1462463376025192, 8774780256151144, 52648681536906856, 315892089221441128, 1895352535328646760

Offset

0,1

Comments

Number of functions expressible by width-2 ordered binary decision diagrams on n+1 variables in a fixed order. - Kiran Tomlinson, Apr 15 2026

References

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..23.

J. T. Butler, Tandem networks of universal cells, IEEE Trans. Computers, C-27 (1978), 785-799. (Annotated scanned copy)

K. K. Maitra, Cascaded switching networks of two-input flexible cells, IEEE Trans. Electron. Computers, C-11 (1962), 136-143.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for linear recurrences with constant coefficients, signature (7,-6).

Formula

G.f.: ( 4-12*x ) / ( (6*x-1)*(x-1) ). - Simon Plouffe in his 1992 dissertation

For n > 0, a(n) = N(n,2,2) where N(n,s,r) is defined in A005608. - Sean A. Irvine, Jul 13 2016

a(n) = 4 * A261399(n+1) = (12*6^n+8)/5. - Alois P. Heinz, Apr 15 2026

E.g.f.: 4*exp(x)*(2 + 3*exp(5*x))/5. - Stefano Spezia, Apr 26 2026

Mathematica

NestList[6#-8&, 4, 20] (* Harvey P. Dale, Mar 29 2018 *)

Crossrefs

Cf. A005608, A005609, A261399.

Sequence in context: A165964 A300279 A321238 * A005495 A052124 A235166

Adjacent sequences: A005615 A005616 A005617 * A005619 A005620 A005621

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Jon E. Schoenfield, Mar 27 2010

More terms and name clarified by Michel Marcus, Apr 15 2026

Status

approved