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A109808
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a(n) = 2*7^(n-1).
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6
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2, 14, 98, 686, 4802, 33614, 235298, 1647086, 11529602, 80707214, 564950498, 3954653486, 27682574402, 193778020814, 1356446145698, 9495123019886, 66465861139202, 465261027974414, 3256827195820898, 22797790370746286, 159584532595224002, 1117091728166568014
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OFFSET
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1,1
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COMMENTS
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Value of Tutte dichromatic polynomial T_G(0,1) where G is the Cartesian product of the paths P_2 and P_n (n>1).
The value of Tutte dichromatic polynomial T_G(0,1) where G is the Cartesian product of the paths P_1 and P_n (n>1) is seen to be 2^(n-1), which is also the number of edge-rooted forests in P_n.
In 1956, Andrzej Schinzel showed that for every n >= 2, a(n) is not a value of Euler's function. - Arkadiusz Wesolowski, Oct 20 2013
Apart from first term 2, these are the numbers that satisfy phi(n) = 3*n/7. - Michel Marcus, Jul 14 2015
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Tanya Khovanova, Recursive Sequences
W. Kook, Edge-rooted forests and alpha-invariant of cone graphs, Discrete Applied Mathematics, Volume 155, Issue 8, 15 April 2007, Pages 1071-1075.
Mitchell Paukner, Lucy Pepin, Manda Riehl, and Jarred Wieser, Pattern Avoidance in Task-Precedence Posets, arXiv:1511.00080 [math.CO], 2015-2016.
Index entries for linear recurrences with constant coefficients, signature (7).
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FORMULA
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a(n) = 2*7^(n-1); a(n) = 7*a(n-1) where a(1) = 2.
G.f.: 2*x/(1 - 7*x). - Philippe Deléham, Nov 23 2008
E.g.f.: 2*(exp(7*x) - 1)/7. - Stefano Spezia, May 29 2021
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MAPLE
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a:= n-> 2*7^(n-1): seq(a(n), n=1..30);
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MATHEMATICA
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2*7^Range[0, 40] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)
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PROG
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(PARI) a(n)=7^n*2/7 \\ Charles R Greathouse IV, Jun 10 2011
(Magma) [2*7^(n-1):n in [1..25]]; // Vincenzo Librandi, Sep 15 2011
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CROSSREFS
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Cf. A000420.
Sequence in context: A204699 A286445 A322262 * A304444 A247481 A037516
Adjacent sequences: A109805 A109806 A109807 * A109809 A109810 A109811
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KEYWORD
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nonn,easy
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AUTHOR
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Woong Kook (andrewk(AT)math.uri.edu), Aug 16 2005
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EXTENSIONS
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Name changed by Arkadiusz Wesolowski, Oct 20 2013
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STATUS
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approved
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