A046639 Length of A001388(n).

1, 2, 2, 4, 6, 7, 10, 12, 18, 25, 31, 41, 56, 73, 96, 128, 171, 226, 302, 399, 533, 704, 937, 1236, 1645, 2170, 2884, 3806, 5059, 6680, 8875, 11725, 15575, 20584, 27332, 36132, 47963, 63420, 84160, 111306, 147673, 195345, 259118, 342831, 454680

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base
• easy

Comments

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

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..1000
• N. Johnston, Further Variants of the “Look-and-Say” Sequence
• Index entries for linear recurrences with constant coefficients, signature (0,2,1,0,-2,-2,0,2,2,0,-1,-1).

Crossrefs

Cf. A005150, A049194.

Programs

Mathematica

p={-1,3,4,1,-2,-4,-4,1,5,1,0,0,-1,0,-1,0,2,1};
q={1,1,0,-2,-2,0,2,2,0,-1,-2,0,1};
gf=Fold[x #1+#2&,0,p]/Fold[x #1+#2&,0,q];
CoefficientList[Series[gf,{x,0,100}],x] (* Peter J. C. Moses, Jun 21 2013 *)
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 *)

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

Formula

From Colin Barker, Jul 01 2020: (Start)

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)).

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.

(End)