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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 (list; graph; refs; listen; history; text; internal format)
 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 G. C. Greubel, Table of n, a(n) for n = 1..1000 Martin Burtscher, Igor Szczyrba, RafaĆ Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5. Index entries for linear recurrences with constant coefficients, signature (1,1,1). 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:=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 CROSSREFS Cf. A000073, A000213, A001590, A003265, A056816, A081172, A001644. Sequence in context: A325436 A346777 A338585 * A088275 A274836 A322783 Adjacent sequences:  A145024 A145025 A145026 * A145028 A145029 A145030 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, Sep 30 2008 STATUS approved

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Last modified September 25 12:38 EDT 2021. Contains 347654 sequences. (Running on oeis4.)