622766746260\
22472480156659330677754354367566446245619515011589704068286465445

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The Tribonacci constant, is such that 1/(1-x-x^2-x^3) once expanded into
a series will give coefficients proportional to approx. c**n
and c = (to 1000 digits).

1.8392867552141611325518525646532866004241787460975922467787586394042032220819\
664257384354194283070141419798268592409741641784507465074369438315458204995137\
962496555396446136661215402779726781189410412116092232821559560718167121823659\
866522733785378156969892521173957914132287210618789840852549569311453491349853\
459576175035965221323814247272722417358187700069790551025490449657107425265477\
228110065989375556363093330528262357538519719942991453008254663977472900587005\
974481391931672825848839626332970700687236831127837750250557122275153259578946\
560570686422283918659698294691356239220443192476147068811451726766712743964146\
212571843342662340390218352494591033227231061513286997030808036302223324997105\
243107472354231399744381826565607351940357874911762680524537079221110849710806\
876410050156541475662235008885665949715821834184868714802901255436993480513679\
165025853053878276666126224317766358200942985505387325991651787730184472388604\
26222324857820792721049160181783725613203439814302274533997621231

/ 19 1/2\1/3 4
|---- + 1/9 33 | + ----------------------- + 1/3
\ 27 / / 19 1/2\1/3
9 |---- + 1/9 33 |
\ 27 /

in fact the n'th Tribonacci number is given by this EXACT formula.
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See : http://www.labri.u-bordeaux.fr/~loeb/book/92pl.html

Comment calculer le nieme nombre de Tribonacci

Resume of a conference given in 1993 (Universite Bordeaux I, LaBRI).

1/2 1/3 1/2 1/3 n 1/2 1/3
(1/3 (19 + 3 33 ) + 1/3 (19 - 3 33 ) + 1/3) (586 + 102 33 )
3 ---------------------------------------------------------------------------
1/2 2/3 1/2 1/3
(586 + 102 33 ) + 4 - 2 (586 + 102 33 )

To get the actual n'th Tribonacci number just round the result to the
nearest integer.

Here is the formula '