A047230 Numbers that are congruent to {3, 4} mod 6.

3, 4, 9, 10, 15, 16, 21, 22, 27, 28, 33, 34, 39, 40, 45, 46, 51, 52, 57, 58, 63, 64, 69, 70, 75, 76, 81, 82, 87, 88, 93, 94, 99, 100, 105, 106, 111, 112, 117, 118, 123, 124, 129, 130, 135, 136, 141, 142, 147, 148

Offset

1,1

Comments

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

Links

David Lovler, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = 6*n - a(n-1) - 5 (with a(1)=3). - Vincenzo Librandi, Aug 05 2010

From R. J. Mathar, Oct 08 2011: (Start)

a(n) = 3*n - 1 - (-1)^n.

G.f.: ( x*(3+x+2*x^2) ) / ( (1+x)*(x-1)^2 ).

(End)

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(12*sqrt(3)) + log(2)/3 - log(3)/4. - Amiram Eldar, Dec 13 2021

E.g.f.: 2 + 3*x*exp(x) - 2*cosh(x). - David Lovler, Aug 25 2022

Mathematica

LinearRecurrence[{1, 1, -1}, {3, 4, 9}, 50] (* Harvey P. Dale, Dec 04 2018 *)

Prog

(PARI) a(n) = 3*n - 1 - (-1)^n \\ David Lovler, Aug 25 2022

Crossrefs

Sequence in context: A129783 A301919 A093513 * A277138 A327282 A126269

Adjacent sequences: A047227 A047228 A047229 * A047231 A047232 A047233

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved