A214828 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 6.

1, 6, 6, 13, 25, 44, 82, 151, 277, 510, 938, 1725, 3173, 5836, 10734, 19743, 36313, 66790, 122846, 225949, 415585, 764380, 1405914, 2585879, 4756173, 8747966, 16090018, 29594157, 54432141, 100116316, 184142614, 338691071, 622950001

Offset

0,2

Comments

See comments in A214727.

Links

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

Martin Burtscher, Igor Szczyrba, Rafał 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.: (1+5*x-x^2)/(1-x-x^2-x^3).

a(n) = -A000073(n) + 5*A000073(n+1) + A000073(n+2). - G. C. Greubel, Apr 24 2019

Mathematica

LinearRecurrence[{1, 1, 1}, {1, 6, 6}, 33] (* Ray Chandler, Dec 08 2013 *)

Prog

(PARI) my(x='x+O('x^40)); Vec((1+5*x-x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 24 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+5*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019
(Sage) ((1+5*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, 6, 6];; 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: A262849 A115014 A168332 * A229828 A141378 A003871

Adjacent sequences: A214825 A214826 A214827 * A214829 A214830 A214831

Keyword

nonn,easy

Author

Abel Amene, Jul 30 2012

Status

approved