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%I #36 Aug 26 2022 10:27:07
%S 3,4,9,10,15,16,21,22,27,28,33,34,39,40,45,46,51,52,57,58,63,64,69,70,
%T 75,76,81,82,87,88,93,94,99,100,105,106,111,112,117,118,123,124,129,
%U 130,135,136,141,142,147,148
%N Numbers that are congruent to {3, 4} mod 6.
%C If a(n) = the n-th Towers of Hanoi move, the smallest disc (#1) is on peg B. (Cf. A047264, A047239). For TOH moves 1 and 2, disc #1 is on peg C. For moves 3 and 4, it's on peg B, and for moves 5 and 6, it's on peg A. The cycle continues CBACBACBA... for moves (7,8), (9,10), (11,12), etc. So disc #1 is on peg B for TOH moves (3, 4, 9, 10, 15, 16, ...). - _Gary W. Adamson_ Jun 22 2012
%H David Lovler, <a href="/A047230/b047230.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 6*n - a(n-1) - 5 (with a(1)=3). - _Vincenzo Librandi_, Aug 05 2010
%F From _R. J. Mathar_, Oct 08 2011: (Start)
%F a(n) = 3*n - 1 - (-1)^n.
%F G.f.: ( x*(3+x+2*x^2) ) / ( (1+x)*(x-1)^2 ).
%F (End)
%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(12*sqrt(3)) + log(2)/3 - log(3)/4. - _Amiram Eldar_, Dec 13 2021
%F E.g.f.: 2 + 3*x*exp(x) - 2*cosh(x). - _David Lovler_, Aug 25 2022
%t LinearRecurrence[{1,1,-1},{3,4,9},50] (* _Harvey P. Dale_, Dec 04 2018 *)
%o (PARI) a(n) = 3*n - 1 - (-1)^n \\ _David Lovler_, Aug 25 2022
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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