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A081172 Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) starting with 1,1,0. 35
1, 1, 0, 2, 3, 5, 10, 18, 33, 61, 112, 206, 379, 697, 1282, 2358, 4337, 7977, 14672, 26986, 49635, 91293, 167914, 308842, 568049, 1044805, 1921696, 3534550, 6501051, 11957297, 21992898, 40451246, 74401441, 136845585, 251698272, 462945298, 851489155 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Completes the set of tribonacci numbers starting with 0's and 1's in the first three terms:

0,0,0 A000004;

0,0,1 A000073;

0,1,0 A001590;

0,1,1 A000073 starting at a(1);

1,0,0 A000073 starting at a(-1);

1,0,1 A001590;

1,1,0 this sequence;

1,1,1 A000213.

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..500

Martin Burtscher, Igor Szczyrba, RafaƂ Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

N. G. Voll, Some identities for four term recurrence relations, Fib. Quart., 51 (2013), 268-273.

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

FORMULA

G.f.: (-1+2*x^2)/(-1 + x + x^2 + x^3). a(n) = A000073(n+2) - 2*A000073(n). - R. J. Mathar, Mar 27 2009

MAPLE

A081172 := proc(n)

    option remember;

    if n <= 2 then

        op(n+1, [1, 1, 0]) ;

    else

        add(procname(n-i), i=1..3) ;

    end if;

end proc: # R. J. Mathar, Aug 09 2012

MATHEMATICA

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

PROG

(PARI) { a1=1; a2=1; a3=0; write("b081172.txt", 0, " ", a1); write("b081172.txt", 1, " ", a2); write("b081172.txt", 2, " ", a3); for(n=3, 500, a=a1+a2+a3; a1=a2; a2=a3; a3=a; write("b081172.txt", n, " ", a) ) } \\ Harry J. Smith, Mar 20 2009

CROSSREFS

Cf. A000004, A000073, A000213, A001590, A020992.

Sequence in context: A195507 A117222 A199594 * A030032 A002661 A216959

Adjacent sequences:  A081169 A081170 A081171 * A081173 A081174 A081175

KEYWORD

nonn,easy

AUTHOR

Harry J. Smith, Apr 19 2003

STATUS

approved

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Last modified July 25 04:48 EDT 2017. Contains 289779 sequences.