A214826 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 4.

1, 4, 4, 9, 17, 30, 56, 103, 189, 348, 640, 1177, 2165, 3982, 7324, 13471, 24777, 45572, 83820, 154169, 283561, 521550, 959280, 1764391, 3245221, 5968892, 10978504, 20192617, 37140013, 68311134, 125643764, 231094911, 425049809

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+3*x-x^2)/(1-x-x^2-x^3).

a(n) = K(n) - 2*T(n+1) + 5*T(n), where K(n) = A001644(n) and T(n) = A000073(n+1). - G. C. Greubel, Apr 23 2019

Mathematica

LinearRecurrence[{1, 1, 1}, {1, 4, 4}, 33] (* Ray Chandler, Dec 08 2013 *)

Prog

(PARI) my(x='x+O('x^40)); Vec((1+3*x-x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 23 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+3*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 23 2019
(Sage) ((1+3*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 23 2019
(GAP) a:=[1, 4, 4];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 23 2019

Crossrefs

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

Sequence in context: A203003 A339427 A319646 * A135065 A067553 A112683

Adjacent sequences: A214823 A214824 A214825 * A214827 A214828 A214829

Keyword

nonn,easy

Author

Abel Amene, Jul 29 2012

Status

approved