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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

Mathematica

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

PARI

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

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