cp's OEIS Frontend

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

%I A336337 #12 Aug 19 2022 05:46:50
%S A336337 0,3,12,41,132,413,1272,3881,11772,35573,107232,322721,970212,2914733,
%T A336337 8752392,26273561,78853452,236625893,710008752,2130288401,6391389492,
%U A336337 19175217053,57527748312,172587439241,517770706332,1553328896213,4660020243072,13980127838081
%N A336337 Total number of records over all length n ternary words (words on alphabet {0,1,2}).
%C A336337 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.
%H A336337 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F A336337 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.
%F A336337 a(n) = Sum_{k=0..3} A285852(n,k)*k.
%F A336337 a(n) = 11/2*3^(n-1)-2^n-1/2, n>0. - _R. J. Mathar_, Aug 19 2022
%t A336337 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]
%Y A336337 Cf. A055010, A285852.
%K A336337 nonn,easy
%O A336337 0,2
%A A336337 _Geoffrey Critzer_, Jul 18 2020