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A081172
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Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = 1, a(2) = 0.
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37
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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
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OFFSET
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0,4
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COMMENTS
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The name "tribonacci number" is less well-defined than "Fibonacci number". The sequence A000073 (which begins 0, 0, 1) is probably the most important version, but the name has also been applied to A000213, A001590, and A081172. - N. J. A. Sloane, Jul 25 2024
Completes the set of tribonacci numbers starting with 0's and 1's in the first three terms:
1,1,0 this sequence;
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LINKS
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FORMULA
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G.f.: (1-2*x^2)/(1 - x - x^2 - x^3).
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MAPLE
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option remember;
if n <= 2 then
op(n+1, [1, 1, 0]) ;
else
add(procname(n-i), i=1..3) ;
end if;
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MATHEMATICA
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PROG
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(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
(PARI) my(x='x+O('x^40)); Vec((1-2*x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 23 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-2*x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 23 2019
(Sage) ((1-2*x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 23 2019
(GAP) a:=[1, 1, 0];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 23 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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