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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 (list; graph; refs; listen; history; text; internal format)
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

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*(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

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

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Last modified December 16 04:05 EST 2019. Contains 330013 sequences. (Running on oeis4.)