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

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

0,2

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<j.

Links

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

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

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]

Crossrefs

Cf. A055010, A285852.

Sequence in context: A053043 A263102 A038345 * A127120 A325482 A017940

Adjacent sequences: A336334 A336335 A336336 * A336338 A336339 A336340

Keyword

nonn,easy

Author

Geoffrey Critzer, Jul 18 2020

Status

approved