

A109808


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


8



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



FORMULA

a(n) = 2*7^(n1); a(n) = 7*a(n1) where a(1) = 2.
Sum_{n>=1} 1/a(n) = 7/12.
Sum_{n>=1} (1)^(n+1)/a(n) = 7/16.
Product_{n>=1} (1  1/a(n)) = A132023. (End)


MAPLE

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


MATHEMATICA



PROG



CROSSREFS



KEYWORD

nonn,easy


AUTHOR

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


EXTENSIONS



STATUS

approved



