A122553 a(0)=1, a(n)=3 for n > 0.

1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset

0,2

Comments

Continued fraction for ((sqrt(13) - 1))/2.

Decimal expansion of 4/30. - Alonso del Arte, Aug 16 2012

4/3 is the volume of the regular octahedron inscribed in the unit-radius sphere. - Amiram Eldar, Jun 02 2023

Links

Table of n, a(n) for n=0..104.

Jun Yan, Results on pattern avoidance in parking functions, arXiv:2404.07958 [math.CO], 2024. See p. 4.

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

Formula

a(n) = 3 - 2*0^n.

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

Sum_{n >= 0} a(n)*10^(-n) = 4/3.

From Amiram Eldar, Jun 05 2021: (Start)

4/3 = Product_{k>=1} (1 + 1/2^(2^k)).

4/3 = Sum_{k>=0} binomial(2*k,k)/((k+2)*4^k). (End)

Mathematica

RealDigits[4/3, 10, 105][[1]] (* Alonso del Arte, Aug 16 2012 *)
PadRight[{1}, 120, 3] (* Harvey P. Dale, Jul 21 2023 *)

Prog

(PARI) a(n)=(n>=0)+2*(n>0) \\ Jaume Oliver Lafont, Mar 26 2009

Crossrefs

Cf. A118273 (cube), A339259 (regular icosahedron), A363437 (regular tetrahedron), A363438 (regular dodecahedron).

Sequence in context: A010701 A290858 A174971 * A157831 A032552 A087717

Adjacent sequences: A122550 A122551 A122552 * A122554 A122555 A122556

Keyword

nonn,cofr,easy,cons,changed

Author

Philippe Deléham, Sep 20 2006

Status

approved