OFFSET
0,2
COMMENTS
Continued fraction for (sqrt(13) - 1)/2 = A223139.
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
REFERENCES
Calvin C. Clawson, Mathematical Mysteries, The Beauty and Magic of Numbers, Springer, 2013, pp. 95-96, 224.
LINKS
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)
Sum_{k>0} 3*k/4^k = 4/3 [Nicole Oresme]. - Stefano Spezia, Jun 27 2024
K_{n>=3} n/(n-2) = 4/3 (see Clawson at p. 224). - Stefano Spezia, Jul 01 2024
E.g.f.: 3*exp(x) - 2. - Elmo R. Oliveira, Aug 05 2024
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
KEYWORD
AUTHOR
Philippe Deléham, Sep 20 2006
STATUS
approved