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A006043 A traffic light problem: expansion of 2/(1 - 3*x)^3.
(Formerly M2107)
6
2, 18, 108, 540, 2430, 10206, 40824, 157464, 590490, 2165130, 7794468, 27634932, 96722262, 334807830, 1147912560, 3902902704, 13172296626, 44165935746, 147219785820, 488149816140, 1610894393262, 5292938720718 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Column 2 of square array A152818. - Omar E. Pol, Jan 05 2009

In [Bach et al., Section 9], 2*a(n-2) counts the "small diagrams". - Eric M. Schmidt, Sep 23 2017

REFERENCES

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Eric Bach, Jeremie Dusart, Lisa Hellerstein, Devorah Kletenik, Submodular Goal Value of Boolean Functions, arXiv:1702.04067 [cs.DM], 2017.

F. A. Haight, Overflow at a traffic light, Biometrika, 46 (1959), 420-424.

F. A. Haight, Overflow at a traffic light, Biometrika, 46 (1959), 420-424. (Annotated scanned copy)

F. A. Haight, Letter to N. J. A. Sloane, n.d.

Index entries for linear recurrences with constant coefficients, signature (9,-27,27).

FORMULA

a(n) = (n+2)*(n+1)*3^n. - Zerinvary Lajos, Apr 25 2007, corrected by R. J. Mathar, Mar 14 2011

a(n) = 2*A027472(n+3) = A116138(n+1)/3. - R. J. Mathar, Mar 14 2011

a(n) = 2*A000217(n+1)*A000244(n). - Zak Seidov, Mar 14 2011

MAPLE

seq((n+2)*(n+1)*3^n, n=0..23); # Zerinvary Lajos, Apr 25 2007

MATHEMATICA

f[n_] := (n + 2) (n + 1) 3^n; Array[f, 22, 0] (* Or *)

CoefficientList[Series[2/(1 - 3 x)^3, {x, 0, 21}], x] (* Robert G. Wilson v *)

LinearRecurrence[{9, -27, 27}, {2, 18, 108}, 30] (* Harvey P. Dale, Apr 27 2017 *)

PROG

(PARI) a(n)=(n+2)*(n+1)*3^n \\ Charles R Greathouse IV, Mar 16, 2011

(MAGMA)[(n+2)*(n+1)*3^n: n in [0..30]]; // Vincenzo Librandi, Aug 15 2011

CROSSREFS

Cf. A006044, A000142, A152818, A154120. - Omar E. Pol, Jan 05 2009

Sequence in context: A005969 A094251 A101570 * A112328 A038721 A064837

Adjacent sequences:  A006040 A006041 A006042 * A006044 A006045 A006046

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Simon Plouffe

STATUS

approved

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Last modified March 21 22:19 EDT 2019. Contains 321382 sequences. (Running on oeis4.)