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%I #25 Mar 08 2022 15:11:22
%S 1,2,2,4,6,7,10,12,18,25,31,41,56,73,96,128,171,226,302,399,533,704,
%T 937,1236,1645,2170,2884,3806,5059,6680,8875,11725,15575,20584,27332,
%U 36132,47963,63420,84160,111306,147673,195345,259118,342831,454680
%N Length of A001388(n).
%C The average multiplicative growth from the n-th term to the (n+1)st term is the largest root of x^3 - x - 1, which is approximately 1.324718. - _Nathaniel Johnston_, Jan 13 2011
%H Peter J. C. Moses, <a href="/A046639/b046639.txt">Table of n, a(n) for n = 1..1000</a>
%H N. Johnston, <a href="http://www.njohnston.ca/2011/01/further-variants-of-the-look-and-say-sequence/">Further Variants of the “Look-and-Say” Sequence</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1,0,-2,-2,0,2,2,0,-1,-1).
%F From _Colin Barker_, Jul 01 2020: (Start)
%F G.f.: x*(1 + 2*x - x^3 - x^5 + x^8 + 5*x^9 + x^10 - 4*x^11 - 4*x^12 - 2*x^13 + x^14 + 4*x^15 + 3*x^16 - x^17) / ((1 - x)*(1 + x)*(1 + x^2)*(1 - x^2 - x^3)*(1 - x^2 + x^5)).
%F a(n) = 2*a(n-2) + a(n-3) - 2*a(n-5) - 2*a(n-6) + 2*a(n-8) + 2*a(n-9) - a(n-11) - a(n-12) for n>18.
%F (End)
%t p={-1,3,4,1,-2,-4,-4,1,5,1,0,0,-1,0,-1,0,2,1};
%t q={1,1,0,-2,-2,0,2,2,0,-1,-2,0,1};
%t gf=Fold[x #1+#2&,0,p]/Fold[x #1+#2&,0,q];
%t CoefficientList[Series[gf,{x,0,100}],x] (* _Peter J. C. Moses_, Jun 21 2013 *)
%t LinearRecurrence[{0,2,1,0,-2,-2,0,2,2,0,-1,-1},{1,2,2,4,6,7,10,12,18,25,31,41,56,73,96,128,171,226},50] (* _Harvey P. Dale_, Mar 08 2022 *)
%o (PARI) Vec(x*(1 + 2*x - x^3 - x^5 + x^8 + 5*x^9 + x^10 - 4*x^11 - 4*x^12 - 2*x^13 + x^14 + 4*x^15 + 3*x^16 - x^17) / ((1 - x)*(1 + x)*(1 + x^2)*(1 - x^2 - x^3)*(1 - x^2 + x^5)) + O(x^50)) \\ _Colin Barker_, Jul 01 2020
%Y Cf. A005150, A049194.
%K nonn,base,easy
%O 1,2
%A _David W. Wilson_
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