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A214827
a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 5.
15
1, 5, 5, 11, 21, 37, 69, 127, 233, 429, 789, 1451, 2669, 4909, 9029, 16607, 30545, 56181, 103333, 190059, 349573, 642965, 1182597, 2175135, 4000697, 7358429, 13534261, 24893387, 45786077, 84213725, 154893189, 284892991, 523999905
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.: (x^2-4*x-1)/(x^3+x^2+x-1).
a(n) = -A000073(n) + 4*A000073(n+1) + A000073(n+2). - R. J. Mathar, Jul 29 2012
MATHEMATICA
LinearRecurrence[{1, 1, 1}, {1, 5, 5}, 40] (* Ray Chandler, Dec 08 2013 *)
PROG
(PARI) my(x='x+O('x^40)); Vec((1+4*x-x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 24 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+4*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019
(Sage) ((1+4*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 24 2019
(GAP) a:=[1, 5, 5];; 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
KEYWORD
nonn,easy
AUTHOR
Abel Amene, Jul 29 2012
STATUS
approved