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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 A308700 Adjacent sequences:  A006040 A006041 A006042 * A006044 A006045 A006046 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified January 28 22:40 EST 2020. Contains 331328 sequences. (Running on oeis4.)