

A047239


Numbers that are congruent to {1, 2} mod 6.


7



1, 2, 7, 8, 13, 14, 19, 20, 25, 26, 31, 32, 37, 38, 43, 44, 49, 50, 55, 56, 61, 62, 67, 68, 73, 74, 79, 80, 85, 86, 91, 92, 97, 98, 103, 104, 109, 110, 115, 116, 121, 122, 127, 128, 133, 134, 139, 140, 145, 146, 151
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OFFSET

1,2


COMMENTS

If a(n) is the nth Towers of Hanoi move, the smallest disc (#1) is on peg C. If n == (3,4) (mod 6), disc #1 is on peg B; and if n == (0,5) (mod 6) disc #1 is on peg A. Disc #1 moves every 1,3,5,7,...th move in a rotational cycle CBACBACBA such that it's on peg C the first TOH move and stays there for the 2nd move (in which case disc #2 moves). Therefore disc #1 is on peg C in moves (1, 2, 7, 8, 13, ...).  Gary W. Adamson, Jun 22 2012
Conjecture: a(n) is the least positive integer > a(n1) that is not equal to a(i) + a(j) + a(k) for any i <= j <= k <= n.  Clark Kimberling, Oct 09 2019


LINKS

Table of n, a(n) for n=1..51.
Index entries for linear recurrences with constant coefficients, signature (1,1,1).


FORMULA

a(n) = 3*(n1)  (1)^n.  Rolf Pleisch, Aug 04 2009
a(n) = 6*n  a(n1)  9 (with a(1)=1).  Vincenzo Librandi, Aug 05 2010
G.f. x*(1+x+4*x^2) / ( (1+x)*(x1)^2 ).  R. J. Mathar, Oct 08 2011
a(n) = a(n1) + a(n2)  a(n3) with a(1)=1, a(2)=2, a(3)=7.  Harvey P. Dale, Nov 23 2011
E.g.f.: 4 + 3*exp(x)*(x  1)  exp(x).  Stefano Spezia, Oct 09 2019


MATHEMATICA

Select[Range[200], MemberQ[{1, 2}, Mod[#, 6]]&] (* or *) LinearRecurrence[ {1, 1, 1}, {1, 2, 7}, 80] (* Harvey P. Dale, Nov 23 2011 *)


CROSSREFS

Cf. A047264.
Sequence in context: A037073 A329407 A329408 * A329410 A246389 A329409
Adjacent sequences: A047236 A047237 A047238 * A047240 A047241 A047242


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


STATUS

approved



