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!)
A214827 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 5. 15
1, 5, 5, 11, 21, 37, 69, 127, 233, 429, 789, 1451, 2669, 4909, 9029, 16607, 30545, 56181, 103333, 190059, 349573, 642965, 1182597, 2175135, 4000697, 7358429, 13534261, 24893387, 45786077, 84213725, 154893189, 284892991, 523999905 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See comments in A214727.

LINKS

Robert Price, Table of n, a(n) for n = 0..1000

Martin Burtscher, Igor Szczyrba, RafaƂ Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

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

FORMULA

G.f.: (x^2-4*x-1)/(x^3+x^2+x-1).

a(n) = -A000073(n) + 4*A000073(n+1) + A000073(n+2). - R. J. Mathar, Jul 29 2012

MATHEMATICA

LinearRecurrence[{1, 1, 1}, {1, 5, 5}, 40] (* Ray Chandler, Dec 08 2013 *)

PROG

(PARI) my(x='x+O('x^40)); Vec((1+4*x-x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 24 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+4*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019

(Sage) ((1+4*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 24 2019

(GAP) a:=[1, 5, 5];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 24 2019

CROSSREFS

Cf. A000213, A000288, A000322, A000383, A060455, A136175, A141036, A141523, A214825-A214831.

Sequence in context: A164930 A298165 A301800 * A298955 A299591 A173316

Adjacent sequences:  A214824 A214825 A214826 * A214828 A214829 A214830

KEYWORD

nonn,easy

AUTHOR

Abel Amene, Jul 29 2012

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 September 24 12:31 EDT 2021. Contains 347642 sequences. (Running on oeis4.)