A145027 a(n) = a(n-1) + a(n-2) + a(n-3) with a(1) = 2, a(2) = 3, a(3) = 4.

2, 3, 4, 9, 16, 29, 54, 99, 182, 335, 616, 1133, 2084, 3833, 7050, 12967, 23850, 43867, 80684, 148401, 272952, 502037, 923390, 1698379, 3123806, 5745575, 10567760, 19437141, 35750476, 65755377, 120942994, 222448847, 409147218

Offset

1,1

Comments

If the conjectured recurrence in A000382 is correct, then a(n) = A000382(n+2) - A000382(n+1), n>=4. - R. J. Mathar, Jan 30 2011

Links

G. C. Greubel, Table of n, a(n) for n = 1..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

From R. J. Mathar, Jan 30 2011: (Start)

a(n) = -A000073(n-1) + A000073(n) + 2*A000073(n+1).

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

Mathematica

LinearRecurrence[{1, 1, 1}, {2, 3, 4}, 33] (* Ray Chandler, Dec 08 2013 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(x*(1+x)*(2-x)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 22 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x*(1+x)*(2-x)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 22 2019
(Sage) a=(x*(1+x)*(2-x)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Apr 22 2019

Crossrefs

Cf. A000073, A000213, A001590, A003265, A056816, A081172, A001644.

Sequence in context: A325436 A346777 A338585 * A088275 A274836 A322783

Adjacent sequences: A145024 A145025 A145026 * A145028 A145029 A145030

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Sep 30 2008

Status

approved