login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099524 Expansion of 1/(1-5*x-x^3). 0
1, 5, 25, 126, 635, 3200, 16126, 81265, 409525, 2063751, 10400020, 52409625, 264111876, 1330959400, 6707206625, 33800145001, 170331684405, 858365628650, 4325628288251, 21798473125660, 109850731256950, 553579284573001 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A transform of A000351 under the mapping mapping g(x)->(1/(1-x^3))g(x/(1-x^3)).

a(n) equals the number of n-length words on {0,1,2,3,4,5} such that 0 appears only in a run which length is a multiple of 3. - Milan Janjic, Feb 17 2015

LINKS

Table of n, a(n) for n=0..21.

Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3

Index entries for linear recurrences with constant coefficients, signature (5,0,1).

FORMULA

a(n) = 5*a(n-1) + a(n-3).

a(n) = Sum_(k=0..floor(n/3)) binomial(n-2*k, k)*5^(n-3*k).

MATHEMATICA

CoefficientList[Series[1/(1-5x-x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[ {5, 0, 1}, {1, 5, 25}, 30] (* Harvey P. Dale, May 08 2012 *)

CROSSREFS

Cf. A099504.

Sequence in context: A173260 A080516 A033141 * A081916 A307879 A082308

Adjacent sequences:  A099521 A099522 A099523 * A099525 A099526 A099527

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Oct 20 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 December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)