A214831 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 9.
1, 9, 9, 19, 37, 65, 121, 223, 409, 753, 1385, 2547, 4685, 8617, 15849, 29151, 53617, 98617, 181385, 333619, 613621, 1128625, 2075865, 3818111, 7022601, 12916577, 23757289, 43696467, 80370333, 147824089, 271890889, 500085311, 919800289, 1691776489
Offset: 0
Links
- Robert Price, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (1,1,1).
Crossrefs
Programs
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GAP
a:=[1,9,9];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 24 2019
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Magma
R
:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+8*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019 -
Mathematica
LinearRecurrence[{1,1,1},{1,9,9},40] (* Harvey P. Dale, Oct 11 2017 *) -
PARI
Vec((x^2-8*x-1)/(x^3+x^2+x-1) + O(x^40)) \\ Michel Marcus, Jul 08 2014
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SageMath
((1+8*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 24 2019
Formula
G.f.: (1+8*x-x^2)/(1-x-x^2-x^3).
Comments