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A020992 a(n) = a(n-1) + a(n-2) + a(n-3). 52
0, 2, 1, 3, 6, 10, 19, 35, 64, 118, 217, 399, 734, 1350, 2483, 4567, 8400, 15450, 28417, 52267, 96134, 176818, 325219, 598171, 1100208, 2023598, 3721977, 6845783, 12591358, 23159118, 42596259, 78346735, 144102112, 265045106, 487493953, 896641171, 1649180230 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Tribonacci sequence beginning 0, 2, 1.

Pisano period lengths: 1, 4, 13, 8, 31, 52, 48, 16, 39, 124, 110, 104, 168, 48, 403, 32, 96, 156, 360, 248,.... - R. J. Mathar, Aug 10 2012

One bisection is 0, 1, 6, 19, 64, 217, 734, 2483, 8400,.. and the other 2, 3, 10, 35, 118, 399, 1350, 4567,... both with recurrence b(n)=3*b(n-1)+b(n-2)+b(n-3). - R. J. Mathar, Aug 10 2012

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

a(n) = 2*A000073(n+1)-A000073(n). - R. J. Mathar, Aug 22 2008

a(n) = 2*a(n-1) - a(n-4), n>3. - Vincenzo Librandi, Jun 08 2011

MATHEMATICA

LinearRecurrence[{1, 1, 1}, {0, 2, 1}, 100] (* Vladimir Joseph Stephan Orlovsky, Jun 07 2011 *)

PROG

(PARI) x='x+O('x^30); concat([0], Vec(x*(2-x)/(1-x-x^2-x^3))) \\ G. C. Greubel, Feb 09 2018

(Magma) I:=[0, 2, 1]; [n le 3 select I[n] else Self(n-1) + Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Feb 09 2018

CROSSREFS

Cf. A000032, A000073, A001590, A232498, A233554.

Sequence in context: A024866 A076058 A098124 * A025110 A075346 A357844

Adjacent sequences: A020989 A020990 A020991 * A020993 A020994 A020995

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 5 19:04 EST 2022. Contains 358588 sequences. (Running on oeis4.)