login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A094188 Number of levels in the compositions of n with odd summands. 0
1, 0, 3, 2, 8, 10, 23, 36, 69, 116, 208, 356, 621, 1064, 1831, 3126, 5336, 9070, 15395, 26060, 44041, 74280, 125088, 210312, 353113, 592080, 991563, 1658666, 2771624, 4626706, 7716143, 12857076, 21405261, 35608604, 59192176, 98325356 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

Table of n, a(n) for n=2..37.

S. Heubach and T. Mansour, Counting rises, levels and drops in compositions, arXiv:math/0310197 [math.CO], 2003.

Index entries for linear recurrences with constant coefficients, signature (1, 3, -1, -3, -1).

FORMULA

G.f.: (x^2(1-x^2))/((1+x)^2(1-x-x^2)^2).

a(n) = (1/5) * [3nF(n)-4nF(n-1)+7F(n)-10F(n-1)+10(-1)^n], F(n)=A000045(n).

MATHEMATICA

LinearRecurrence[{1, 3, -1, -3, -1}, {1, 0, 3, 2, 8, 10}, 36] (* Jean-François Alcover, Jan 21 2019 *)

CROSSREFS

Cf. A000045.

Sequence in context: A163356 A209360 A095013 * A088551 A301903 A165660

Adjacent sequences:  A094185 A094186 A094187 * A094189 A094190 A094191

KEYWORD

nonn

AUTHOR

Ralf Stephan, May 25 2004

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 25 16:42 EST 2020. Contains 331245 sequences. (Running on oeis4.)