A246518 -id:A246518 - cp's OEIS frontend

A141036 Tribonacci-like sequence; a(0)=2, a(1)=1, a(2)=1, a(n) = a(n-1) + a(n-2) + a(n-3).

2, 1, 1, 4, 6, 11, 21, 38, 70, 129, 237, 436, 802, 1475, 2713, 4990, 9178, 16881, 31049, 57108, 105038, 193195, 355341, 653574, 1202110, 2211025, 4066709, 7479844, 13757578, 25304131, 46541553, 85603262, 157448946, 289593761

Offset: 0

Matt Wynne (matwyn(AT)verizon.net), Jul 30 2008

I used the short MATLAB program from the zip file link altered to produce a Lucas version of the tribonacci numbers.
No term is divisible by 8 or 9. - Vladimir Joseph Stephan Orlovsky, Mar 24 2011
a(A246517(n)) = A246518(n). - Reinhard Zumkeller, Sep 15 2014

Martin Gardner, Mathematical Circus, Random House, New York, 1981, p. 165.

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.
T.-X. He, Impulse Response Sequences and Construction of Number Sequence Identities, J. Int. Seq. 16 (2013) #13.8.2
Index entries for linear recurrences with constant coefficients, signature (1,1,1).

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

a141036 n = a141036_list !! n
a141036_list = 2 : 1 : 1 : zipWith3 (((+) .) . (+))
   a141036_list (tail a141036_list) (drop 2 a141036_list)
-- Reinhard Zumkeller, Sep 15 2014

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

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, 40}] (* Alonso del Arte, Mar 24 2011 *)
LinearRecurrence[{1, 1, 1}, {2, 1, 1}, 40] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)

a(n)=([0,1,0;0,0,1;1,1,1]^n*[2;1;1])[1,1] \\ Charles R Greathouse IV, Jun 15 2015

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

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

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

Corrected offset and indices in formulas, R. J. Mathar, Aug 05 2008

Better name from T. D. Noe, Aug 06 2008

A246517 Indices of primes in A141036.

Original entry on oeis.org

0, 5, 14, 26, 33, 222, 234, 482, 937, 1170, 1290, 1877, 1897, 3413, 6017, 9365, 47470, 48254, 97421, 102057, 119689, 132418, 192517, 194442

Offset: 1

Robert Price, Aug 28 2014

nonn

a(25) > 2*10^5.

A141036(a(n)) = A246518(n).

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Cf. A001590, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A214827-A214829, A243622, A243623, A214831, A141036.

Cf. A049084.

a246517 n = a246517_list !! (n-1)
a246517_list = filter ((== 1) . a010051'' . a141036) [0..]
-- Reinhard Zumkeller, Sep 15 2014

a={2,1,1}; Print[0]; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[3]]=sum]

cp's OEIS Frontend

A141036 Tribonacci-like sequence; a(0)=2, a(1)=1, a(2)=1, a(n) = a(n-1) + a(n-2) + a(n-3).

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