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 A073717 a(n) = T(2n+1), where T(n) are the tribonacci numbers A000073. 4
 0, 1, 4, 13, 44, 149, 504, 1705, 5768, 19513, 66012, 223317, 755476, 2555757, 8646064, 29249425, 98950096, 334745777, 1132436852, 3831006429, 12960201916, 43844049029, 148323355432, 501774317241, 1697490356184, 5742568741225 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,1,1). FORMULA a(n) = 3*a(n-1) +a(n-2) +a(n-3), a(0)=0, a(1)=1, a(2)=4. G.f.: x*(1+x)/(1-3*x-x^2-x^3). a(n+1) = Sum_{0<=k<=n} A216182(n,k). - Philippe Deléham, Mar 11 2013 a(n) = A113300(n-1) + A113300(n). - R. J. Mathar, Jul 04 2019 MATHEMATICA CoefficientList[Series[(x+x^2)/(1-3x-x^2-x^3), {x, 0, 30}], x] LinearRecurrence[{3, 1, 1}, {0, 1, 4}, 30] (* Harvey P. Dale, Sep 07 2015 *) PROG (Magma) [n le 3 select (n-1)^2 else 3*Self(n-1) +Self(n-2) +Self(n-3): n in [1..31]]; // G. C. Greubel, Nov 19 2021 (Sage) def A073717_list(prec): P. = PowerSeriesRing(ZZ, prec) return P( x*(1+x)/(1-3*x-x^2-x^3) ).list() A073717_list(30) # G. C. Greubel, Nov 19 2021 CROSSREFS Cf. A000073, A099463, A113300. Row sums of A216182. Sequence in context: A027125 A027127 A326329 * A149427 A290907 A252933 Adjacent sequences: A073714 A073715 A073716 * A073718 A073719 A073720 KEYWORD easy,nonn AUTHOR Mario Catalani (mario.catalani(AT)unito.it), Aug 05 2002 STATUS approved

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Last modified September 26 02:15 EDT 2023. Contains 365649 sequences. (Running on oeis4.)