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A145027
a(n) = a(n-1) + a(n-2) + a(n-3) with a(1) = 2, a(2) = 3, a(3) = 4.
3
2, 3, 4, 9, 16, 29, 54, 99, 182, 335, 616, 1133, 2084, 3833, 7050, 12967, 23850, 43867, 80684, 148401, 272952, 502037, 923390, 1698379, 3123806, 5745575, 10567760, 19437141, 35750476, 65755377, 120942994, 222448847, 409147218
OFFSET
1,1
COMMENTS
If the conjectured recurrence in A000382 is correct, then a(n) = A000382(n+2) - A000382(n+1), n>=4. - R. J. Mathar, Jan 30 2011
LINKS
Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
FORMULA
From R. J. Mathar, Jan 30 2011: (Start)
a(n) = -A000073(n-1) + A000073(n) + 2*A000073(n+1).
G.f. x*(1+x)*(2-x)/(1-x-x^2-x^3). (End)
MATHEMATICA
LinearRecurrence[{1, 1, 1}, {2, 3, 4}, 33] (* Ray Chandler, Dec 08 2013 *)
PROG
(PARI) my(x='x+O('x^30)); Vec(x*(1+x)*(2-x)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 22 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x*(1+x)*(2-x)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 22 2019
(Sage) a=(x*(1+x)*(2-x)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Apr 22 2019
KEYWORD
nonn
AUTHOR
STATUS
approved