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A214826
a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 4.
5
1, 4, 4, 9, 17, 30, 56, 103, 189, 348, 640, 1177, 2165, 3982, 7324, 13471, 24777, 45572, 83820, 154169, 283561, 521550, 959280, 1764391, 3245221, 5968892, 10978504, 20192617, 37140013, 68311134, 125643764, 231094911, 425049809
OFFSET
0,2
COMMENTS
See Comments in A214727.
LINKS
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.
FORMULA
G.f.: (1+3*x-x^2)/(1-x-x^2-x^3).
a(n) = K(n) - 2*T(n+1) + 5*T(n), where K(n) = A001644(n) and T(n) = A000073(n+1). - G. C. Greubel, Apr 23 2019
MATHEMATICA
LinearRecurrence[{1, 1, 1}, {1, 4, 4}, 33] (* Ray Chandler, Dec 08 2013 *)
PROG
(PARI) my(x='x+O('x^40)); Vec((1+3*x-x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 23 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+3*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 23 2019
(Sage) ((1+3*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 23 2019
(GAP) a:=[1, 4, 4];; 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
KEYWORD
nonn,easy
AUTHOR
Abel Amene, Jul 29 2012
STATUS
approved