A073717 a(n) = T(2n+1), where T(n) are the tribonacci numbers A000073.

0, 1, 4, 13, 44, 149, 504, 1705, 5768, 19513, 66012, 223317, 755476, 2555757, 8646064, 29249425, 98950096, 334745777, 1132436852, 3831006429, 12960201916, 43844049029, 148323355432, 501774317241, 1697490356184, 5742568741225

Offset

0,3

Comments

In general, the bisection of a third-order linear recurrence with signature (x,y,z) will result in a third-order recurrence with signature (x^2 + 2*y, 2*z*x - y^2, z^2). - Gary Detlefs, May 29 2024

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,1,1).

Formula

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

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

a(n+1) = Sum_{k=0..n} A216182(n,k). - Philippe Deléham, Mar 11 2013

a(n) = A113300(n-1) + A113300(n). - R. J. Mathar, Jul 04 2019

Mathematica

CoefficientList[Series[(x+x^2)/(1-3x-x^2-x^3), {x, 0, 30}], x]
LinearRecurrence[{3, 1, 1}, {0, 1, 4}, 30] (* Harvey P. Dale, Sep 07 2015 *)

Prog

(Magma) [n le 3 select (n-1)^2 else 3*Self(n-1) +Self(n-2) +Self(n-3): n in [1..31]]; // G. C. Greubel, Nov 19 2021
(Sage)
def A073717_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x*(1+x)/(1-3*x-x^2-x^3) ).list()
A073717_list(30) # G. C. Greubel, Nov 19 2021

Crossrefs

Cf. A000073, A099463, A113300.

Row sums of A216182.

Sequence in context: A027125 A027127 A326329 * A149427 A290907 A252933

Adjacent sequences: A073714 A073715 A073716 * A073718 A073719 A073720

Keyword

easy,nonn

Author

Mario Catalani (mario.catalani(AT)unito.it), Aug 05 2002

Status

approved