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

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143447 Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=4. 3
1, 3, 5, 7, 9, 11, 17, 27, 41, 59, 81, 115, 169, 251, 369, 531, 761, 1099, 1601, 2339, 3401, 4923, 7121, 10323, 15001, 21803, 31649, 45891, 66537, 96539, 140145, 203443, 295225, 428299, 621377, 901667, 1308553, 1899003, 2755601, 3998355, 5801689, 8418795 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is also the number of length n ternary words with at least 4 0-digits between any other digits.

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=9, 3*a(n-9) equals the number of 3-colored compositions of n with all parts >=5, such that no adjacent parts have the same color. - Milan Janjic, Nov 27 2011

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,2).

FORMULA

G.f.: 1/(x^4*(1-x-2*x^5)).

G.f.: Q(0)/(2*x^4) -1/x -1/x^2 -1/x^3 -1/x^4, where Q(k) = 1 + 1/(1 - x*(2*k+1 + 2*x^4)/( x*(2*k+2 + 2*x^4) + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Aug 29 2013

a(n) = 2n+1 if n<=5, else a(n) = a(n-1) + 2a(n-5). - Milan Janjic, Mar 09 2015

MAPLE

a:= proc(k::nonnegint) local n, i, j; if k=0 then unapply(3^n, n) else unapply((Matrix(k+1, (i, j)-> if (i=j-1) or j=1 and i=1 then 1 elif j=1 and i=k+1 then 2 else 0 fi)^(n+k))[1, 1], n) fi end(4): seq(a(n), n=0..54);

MATHEMATICA

Series[1/(1-x-2*x^5), {x, 0, 54}] // CoefficientList[#, x]& // Drop[#, 4]& (* Jean-François Alcover, Feb 13 2014 *)

CROSSREFS

4th column of A143453.

Sequence in context: A201644 A064076 A050842 * A152484 A071643 A039578

Adjacent sequences:  A143444 A143445 A143446 * A143448 A143449 A143450

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 16 2008

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 22 08:57 EST 2017. Contains 295076 sequences.