cp's OEIS Frontend

A285852 Rectangular array read by rows: T(n,k) is the number of words of length n on alphabet {0,1,2} that have exactly k records, n>=0, 0<=k<=3.

%I A285852 #19 Jul 22 2020 16:49:24
%S A285852 1,0,0,0,0,3,0,0,0,6,3,0,0,14,12,1,0,36,39,6,0,98,120,25,0,276,363,90,
%T A285852 0,794,1092,301,0,2316,3279,966,0,6818,9840,3025,0,20196,29523,9330,0,
%U A285852 60074,88572,28501,0,179196,265719,86526
%N A285852 Rectangular array read by rows:  T(n,k) is the number of words of length n on alphabet {0,1,2} that have exactly k records, n>=0, 0<=k<=3.
%C A285852 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 A285852 Philippe Flajolet and Robert Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html">Analytic Combinatorics</a>, Cambridge Univ. Press, 2009.
%F A285852 G.f.: Product_{j=1..3} (1 + y*x/(1 - j*x)).  Generally for words on alphabet {0,1,...,r} the o.g.f. is Product_{j=1..r} (1 + y*x/(1 - j*x)).
%e A285852 1,    0,    0,   0;
%e A285852 0,    3,    0,   0;
%e A285852 0,    6,    3,   0;
%e A285852 0,   14,   12,   1;
%e A285852 0,   36,   39,   6;
%e A285852 0,   98,  120,  25;
%e A285852 0,  276,  363,  90;
%e A285852 0,  794, 1092, 301;
%e A285852 0, 2316, 3279, 966;
%t A285852 nn = 12;CoefficientList[Series[Product[1 + u z/(1 - j z), {j, 1, 3}], {z, 0, nn}], {z,u}] // Grid
%Y A285852 Column k=0 gives A000007.
%Y A285852 Column k=1 gives A001550.
%Y A285852 Column k=2 gives A029858.
%Y A285852 Column k=3 gives A000392.
%Y A285852 Row sums give A000244.
%K A285852 nonn,tabf
%O A285852 0,6
%A A285852 _Geoffrey Critzer_, Apr 27 2017