login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A094953 Triangle T(n,m) read by rows: number of rises (drops) in the compositions of n with m parts, m>=2. 5
1, 1, 2, 2, 4, 3, 2, 8, 9, 4, 3, 12, 21, 16, 5, 3, 18, 39, 44, 25, 6, 4, 24, 66, 96, 80, 36, 7, 4, 32, 102, 184, 200, 132, 49, 8, 5, 40, 150, 320, 430, 372, 203, 64, 9, 5, 50, 210, 520, 830, 888, 637, 296, 81, 10, 6, 60, 285, 800, 1480, 1884, 1673, 1024, 414, 100, 11, 6 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

Table of n, a(n) for n=2..68.

S. Heubach and T. Mansour, Counting rises, levels and drops in compositions

FORMULA

G.f. of m-th column: [(m-1)x^(m+1)]/[(1+x)(1-x)^m].

EXAMPLE

1

1 2

2 4 3

2 8 9 4

3 12 21 16 5

3 18 39 44 25 6

4 24 66 96 80 36 7

PROG

(PARI) T(n, m)=polcoeff((m-1)*x^(m+1)/(1+x)/(1-x)^m, n)

CROSSREFS

Columns 2-4 (+-offset) are A004526, A007590, A007518.

Row sums are A045883, diagonals include n, n^2, (n-1)(n^2-n+2)/2, (n-1)^2(n^+n+6), etc.

Cf. A045927.

Sequence in context: A112155 A209749 A248345 * A122687 A002948 A117113

Adjacent sequences:  A094950 A094951 A094952 * A094954 A094955 A094956

KEYWORD

nonn,tabl

AUTHOR

Ralf Stephan, May 26 2004

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified December 22 00:41 EST 2014. Contains 252326 sequences.