The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A141036

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A141036

Tribonacci-like sequence; a(0)=2, a(1)=1, a(2)=1, a(n) = a(n-1) + a(n-2) + a(n-3).
(history; published version)

#48 by Charles R Greathouse IV at Thu Sep 08 08:45:35 EDT 2022

PROG

(MAGMAMagma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (2-x-2*x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 22 2019

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#47 by Susanna Cuyler at Mon Apr 22 18:07:50 EDT 2019

STATUS

proposed

approved

#46 by Michel Marcus at Mon Apr 22 17:15:00 EDT 2019

STATUS

editing

proposed

#45 by Michel Marcus at Mon Apr 22 17:14:45 EDT 2019

CROSSREFS

Cf. A000073, A000213, A001644 (Lucas tribonacci sequence), A246517, A246518.

STATUS

proposed

editing

#44 by G. C. Greubel at Mon Apr 22 16:25:33 EDT 2019

STATUS

editing

proposed

#43 by G. C. Greubel at Mon Apr 22 16:25:23 EDT 2019

FORMULA

a(0)=2; a(1)=1; a(2)=1; a(n) = a(n-1) + a(n-2) + a(n-3).

a(n)=2*A000213(n)-A000073(n+1). O.g.f.: (-2+x+2x^2)/(-1+x+x^2+x^3). - R. J. Mathar, Aug 04 2008

From R. J. Mathar, Aug 04 2008: (Start)

a(n) = 2*A000213(n) - A000073(n+1).

O.g.f.: (2-x-2*x^2)/(1-x-x^2-x^3). (End)

EXAMPLE

fz(1)=2;fz(2)=1;fz(3)=1;

for k=4:n

fz(k)=fz(k-1)+fz(k-2)+fz(k-3);

end

y=fz(n);

MATHEMATICA

a[0] = 2; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3]; Table[a[n], {n, 0, 2940}] (* Alonso del Arte, Mar 24 2011 *)

LinearRecurrence[{1, 1, 1}, {2, 1, 1}, 10040] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)

PROG

(PARI) my(x='x+O('x^40)); Vec((2-x-2*x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 22 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (2-x-2*x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 22 2019

(Sage) ((2-x-2*x^2)/(1-x-x^2-x^3)).series(x, 41).coefficients(x, sparse=False) # G. C. Greubel, Apr 22 2019

STATUS

approved

editing

#42 by R. J. Mathar at Sun Jan 21 14:45:11 EST 2018

STATUS

editing

approved

#41 by R. J. Mathar at Sun Jan 21 14:45:03 EST 2018

LINKS

T.-X. He, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/He/he13.html">Impulse Response Sequences and Construction of Number Sequence Identities</a>, J. Int. Seq. 16 (2013) #13.8.2

STATUS

approved

editing

#40 by N. J. A. Sloane at Tue Dec 19 02:01:11 EST 2017

STATUS

editing

approved

#39 by N. J. A. Sloane at Tue Dec 19 02:01:08 EST 2017

PROG

(MATLAB) function y=fib(n)

STATUS

approved

editing