

A109808


a(n) = 2*7^(n1).


6



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

1,1


COMMENTS

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^(n1), which is also the number of edgerooted 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


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Tanya Khovanova, Recursive Sequences
W. Kook, Edgerooted forests and alphainvariant of cone graphs, Discrete Applied Mathematics, Volume 155, Issue 8, 15 April 2007, Pages 10711075.
Mitchell Paukner, Lucy Pepin, Manda Riehl, and Jarred Wieser, Pattern Avoidance in TaskPrecedence Posets, arXiv:1511.00080 [math.CO], 20152016.
Index entries for linear recurrences with constant coefficients, signature (7).


FORMULA

a(n) = 2*7^(n1); a(n) = 7*a(n1) 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


MAPLE

a:= n> 2*7^(n1): seq(a(n), n=1..30);


MATHEMATICA

2*7^Range[0, 40] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)


PROG

(PARI) a(n)=7^n*2/7 \\ Charles R Greathouse IV, Jun 10 2011
(Magma) [2*7^(n1):n in [1..25]]; // Vincenzo Librandi, Sep 15 2011


CROSSREFS

Cf. A000420.
Sequence in context: A204699 A286445 A322262 * A304444 A247481 A037516
Adjacent sequences: A109805 A109806 A109807 * A109809 A109810 A109811


KEYWORD

nonn,easy


AUTHOR

Woong Kook (andrewk(AT)math.uri.edu), Aug 16 2005


EXTENSIONS

Name changed by Arkadiusz Wesolowski, Oct 20 2013


STATUS

approved



