cp's OEIS Frontend

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

%I A122553 #52 Aug 06 2024 21:35:54
%S A122553 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,
%T A122553 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,
%U A122553 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
%N A122553 a(0)=1, a(n)=3 for n > 0.
%C A122553 Continued fraction for (sqrt(13) - 1)/2 = A223139.
%C A122553 Decimal expansion of 4/30. - _Alonso del Arte_, Aug 16 2012
%C A122553 4/3 is the volume of the regular octahedron inscribed in the unit-radius sphere. - _Amiram Eldar_, Jun 02 2023
%D A122553 Calvin C. Clawson, Mathematical Mysteries, The Beauty and Magic of Numbers, Springer, 2013, pp. 95-96, 224.
%H A122553 Jun Yan, <a href="https://arxiv.org/abs/2404.07958">Results on pattern avoidance in parking functions</a>, arXiv:2404.07958 [math.CO], 2024. See p. 4.
%H A122553 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A122553 a(n) = 3 - 2*0^n.
%F A122553 G.f.: (1 + 2*x)/(1 - x).
%F A122553 Sum_{n >= 0} a(n)*10^(-n) = 4/3.
%F A122553 From _Amiram Eldar_, Jun 05 2021: (Start)
%F A122553 4/3 = Product_{k>=1} (1 + 1/2^(2^k)).
%F A122553 4/3 = Sum_{k>=0} binomial(2*k,k)/((k+2)*4^k). (End)
%F A122553 Sum_{k>0} 3*k/4^k = 4/3 [Nicole Oresme]. - _Stefano Spezia_, Jun 27 2024
%F A122553 K_{n>=3} n/(n-2) = 4/3 (see Clawson at p. 224). - _Stefano Spezia_, Jul 01 2024
%F A122553 E.g.f.: 3*exp(x) - 2. - _Elmo R. Oliveira_, Aug 05 2024
%t A122553 RealDigits[4/3, 10, 105][[1]] (* _Alonso del Arte_, Aug 16 2012 *)
%t A122553 PadRight[{1},120,3] (* _Harvey P. Dale_, Jul 21 2023 *)
%o A122553 (PARI) a(n)=(n>=0)+2*(n>0) \\ _Jaume Oliver Lafont_, Mar 26 2009
%Y A122553 Cf. A118273 (cube), A339259 (regular icosahedron), A363437 (regular tetrahedron), A363438 (regular dodecahedron).
%Y A122553 Cf. A223139.
%K A122553 nonn,cofr,easy,cons
%O A122553 0,2
%A A122553 _Philippe Deléham_, Sep 20 2006