This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A179999 #40 Oct 14 2024 05:52:25
%S A179999 1,2,2,4,6,8,10,14,18,24,30,40,50,66,82,108,134,176,218,286,354,464,
%T A179999 574,752,930,1218,1506,1972,2438,3192,3946,5166,6386,8360,10334,13528,
%U A179999 16722,21890,27058,35420,43782,57312,70842,92734,114626,150048
%N A179999 Length of the n-th term in the modified Look and Say sequence A110393.
%C A179999 The average multiplicative growth from the n-th term to the (n+1)-st term is sqrt(phi) = 1.272..., where phi = (1+sqrt(5))/2 is the golden ratio, see A139339.
%H A179999 Colin Barker, <a href="/A179999/b179999.txt">Table of n, a(n) for n = 1..1000</a>
%H A179999 N. Johnston, <a href="http://www.nathanieljohnston.com/2011/01/further-variants-of-the-look-and-say-sequence/">Further Variants of the “Look-and-Say” Sequence</a>
%H A179999 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,1,-1).
%F A179999 a(n) = length(A110393(n)).
%F A179999 From _Colin Barker_, Aug 10 2019: (Start)
%F A179999 G.f.: x*(1 + x)*(1 + x - x^2)*(1 - x + x^2) / ((1 - x)*(1 - x^2 - x^4)).
%F A179999 a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) for n>6. (End)
%F A179999 From _A.H.M. Smeets_, Aug 10 2019 (Start)
%F A179999 Limit_{n->oo} a(n+1)/a(n) = (1+phi)/2 = (3+sqrt(5))/4 = A239798 for odd n.
%F A179999 Limit_{n->oo} a(n+1)/a(n) = 2/phi = 4/(1+sqrt(5)) = A134972 for even n.
%F A179999 Limit_{n->oo} a(n+2)/a(n) = (1+phi)/phi = phi = A001622. (End)
%F A179999 For odd n > 1, a(n) = 4*Fibonacci((n + 1)/2) - 2. For even n, a(n) = 2*Fibonacci(n/2 + 2) - 2. - _Ehren Metcalfe_, Aug 10 2019
%e A179999 The 6th term in A110393 is 21112211, so a(6) = 8.
%t A179999 CoefficientList[Series[((1+x) (-1-x+x^2) (1-x+x^2))/((1-x) (-1+x^2+x^4)),{x,0,99}],x] (* _Peter J. C. Moses_, Jun 23 2013 *)
%o A179999 (PARI) Vec(x*(1 + x)*(1 + x - x^2)*(1 - x + x^2) / ((1 - x)*(1 - x^2 - x^4)) + O(x^50)) \\ _Colin Barker_, Aug 10 2019
%Y A179999 Cf. A005341, A049194, A098596, A110393.
%Y A179999 Cf. A001622, A134972, A139339, A239798.
%K A179999 nonn,base,easy
%O A179999 1,2
%A A179999 _Nathaniel Johnston_, Jan 13 2011