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A006043
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A traffic light problem: expansion of 2/(1-3*x)^3.
(Formerly M2107)
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6
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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; internal format)
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OFFSET
| 0,1
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COMMENTS
| Column 2 of square array A152818. [From Omar E. Pol, Jan 05 2009]
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REFERENCES
| F. A. Haight, Overflow at a traffic light, Biometrika, 46 (1959), 420-424.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (9,-27,27).
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FORMULA
| a(n) = (n+2)*(n+1)*3^n. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 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
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MAPLE
| seq((n+2)*(n+1)*3^n, n=0..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007
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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] (* RGWv *)
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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
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CROSSREFS
| Cf. A006044, A000142, A152818, A154120. [From Omar E. Pol, Jan 05 2009]
Sequence in context: A005969 A094251 A101570 * A112328 A038721 A064837
Adjacent sequences: A006040 A006041 A006042 * A006044 A006045 A006046
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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