OFFSET
1,2
COMMENTS
If a(n) is the n-th 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(n-1) that is not equal to a(i) + a(j) + a(k) for any i <= j <= k <= n. - Clark Kimberling, Oct 09 2019
LINKS
FORMULA
a(n) = 3*(n-1) - (-1)^n. - Rolf Pleisch, Aug 04 2009
a(n) = 6*n - a(n-1) - 9 (with a(1)=1). - Vincenzo Librandi, Aug 05 2010
G.f. x*(1+x+4*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
a(n) = a(n-1) + a(n-2) - a(n-3) 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
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/18 + log(2)/3. - Amiram Eldar, Dec 13 2021
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
KEYWORD
nonn
AUTHOR
STATUS
approved