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!)
A099234 A trisection of 1/(1-x-x^4). 6
1, 1, 4, 10, 26, 69, 181, 476, 1252, 3292, 8657, 22765, 59864, 157422, 413966, 1088589, 2862617, 7527704, 19795288, 52054840, 136886433, 359964521, 946583628, 2489191330, 6545722210, 17213011605, 45264335853, 119029728628 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A row of A099233.

Row sums of number triangle A116089. - Paul Barry, Feb 04 2006

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..2382

Milan Janjić, Pascal Matrices and Restricted Words, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.

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

FORMULA

G.f.: 1/(1-x(1+x)^3);

a(n) = sum{k=0..n, binomial(3(n-k), k)};

a(n) = a(n-1)+3a(n-2)+3a(n-3)+a(n-4);

a(n) = A003269(3n).

a(n) = sum{k=0..n, C(3k,n-k)} = sum{k=0..n, C(n,k)C(4k,n)/C(4k,k)}. - Paul Barry, Feb 04 2006

G.f.: 1/(G(0) - x) where G(k) = 1 - (2*k+3)*x/(2*k+1 - x*(k+2)*(2*k+1)/(x*(k+2) - (k+1)/G(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Nov 23 2012

MATHEMATICA

CoefficientList[Series[1/(1-x (1+x)^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{1, 3, 3, 1}, {1, 1, 4, 10}, 30] (* Harvey P. Dale, Jun 05 2011 *)

CROSSREFS

Sequence in context: A200051 A200663 A200464 * A087222 A130583 A240048

Adjacent sequences:  A099231 A099232 A099233 * A099235 A099236 A099237

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 08 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 October 19 12:10 EDT 2021. Contains 348088 sequences. (Running on oeis4.)