login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 1
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, 0, 794, 1092, 301, 0, 2316, 3279, 966, 0, 6818, 9840, 3025, 0, 20196, 29523, 9330, 0, 60074, 88572, 28501, 0, 179196, 265719, 86526 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

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..51.

Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009.

FORMULA

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)).

EXAMPLE

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;

0, 794, 1092, 301;

0, 2316, 3279, 966;

MATHEMATICA

nn = 12; CoefficientList[Series[Product[1 + u z/(1 - j z), {j, 1, 3}], {z, 0, nn}], {z, u}] // Grid

CROSSREFS

Column k=0 gives A000007.

Column k=1 gives A001550.

Column k=2 gives A029858.

Column k=3 gives A000392.

Row sums give A000244.

Sequence in context: A221702 A084681 A261038 * A096528 A161837 A299163

Adjacent sequences: A285849 A285850 A285851 * A285853 A285854 A285855

KEYWORD

nonn,tabf

AUTHOR

Geoffrey Critzer, Apr 27 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 21:15 EST 2022. Contains 358362 sequences. (Running on oeis4.)