cp's OEIS Frontend

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.

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A336337 Total number of records over all length n ternary words (words on alphabet {0,1,2}).

Original entry on oeis.org

0, 3, 12, 41, 132, 413, 1272, 3881, 11772, 35573, 107232, 322721, 970212, 2914733, 8752392, 26273561, 78853452, 236625893, 710008752, 2130288401, 6391389492, 19175217053, 57527748312, 172587439241, 517770706332, 1553328896213, 4660020243072, 13980127838081
Offset: 0

Views

Author

Geoffrey Critzer, Jul 18 2020

Keywords

Comments

A record in a word a_1,a_2,...,a_n is a letter a_j that is larger than all the preceding letters. That is, a_j>a_i for all i

Links

Crossrefs

Cf. A055010, A285852.

Programs

  • Mathematica
    nn = 25; Range[0, nn]!; CoefficientList[Series[D[Product[1 + v z/(1 - j z), {j, 1, 3}], v] /. v -> 1, {z, 0, nn}], z]

Formula

O.g.f.: x*(-3 + 6*x - 2*x^2)/(-1 + 6*x - 11*x^2 + 6*x^3) = d/dy A(x,y)|y=1 where A(x,y) is the o.g.f. for A285852.
a(n) = Sum_{k=0..3} A285852(n,k)*k.
a(n) = 11/2*3^(n-1)-2^n-1/2, n>0. - R. J. Mathar, Aug 19 2022
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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