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 A219021 Sum of cubes of first n terms of Lucas sequence U(4,1) (A001353) divided by sum of their first powers. 2
 1, 13, 172, 2356, 32661, 454329, 6325816, 88099144, 1227032521, 17090245381, 238035989412, 3315412063548, 46177727142301, 643172746439665, 8958240642814960, 124772195953666576, 1737852501591502353, 24205162822158610557, 337134426993071036956, 4695676815022772628676, 65402340983109050660389 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For a Lucas sequence U(k,1), the sum of the cubes of the first n terms is divisible by the sum of the first n terms. This sequence corresponds to the case of k=4. LINKS Colin Barker, Table of n, a(n) for n = 1..875 Index entries for linear recurrences with constant coefficients, signature (19,-76,76,-19,1). FORMULA a(n) = Sum_{k=1..n} A001353(k)^3 / Sum_{k=1..n} A001353(k). a(n) = Sum_{k=1..n} A001353(k)^3 / A061278(n). From Colin Barker, Dec 08 2015: (Start) a(n) = 19*a(n-1)-76*a(n-2)+76*a(n-3)-19*a(n-4)+a(n-5) for n>5. G.f.: x*(1-6*x+x^2) / ((1-x)*(1-14*x+x^2)*(1-4*x+x^2)). (End) MATHEMATICA CoefficientList[Series[(1 - 6 x + x^2)/((1 - x) (1 - 14 x + x^2) (1 - 4 x + x^2)), {x, 0, 33}], x] (* Vincenzo Librandi, Dec 09 2015 *) PROG (PARI) Vec(x*(1-6*x+x^2)/((1-x)*(1-14*x+x^2)*(1-4*x+x^2)) + O(x^30)) \\ Colin Barker, Dec 08 2015 (MAGMA) I:=[1, 13, 172, 2356, 32661]; [n le 5 select I[n] else 19*Self(n-1)-76*Self(n-2)+76*Self(n-3)-19*Self(n-4)+Self(n-5): n in [1..30]]; // Vincenzo Librandi, Dec 09 2015 CROSSREFS Cf. A001353, A219020. Sequence in context: A041314 A275293 A296585 * A065544 A096719 A296677 Adjacent sequences:  A219018 A219019 A219020 * A219022 A219023 A219024 KEYWORD nonn,easy AUTHOR Max Alekseyev, Nov 09 2012 STATUS approved

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Last modified June 6 14:04 EDT 2020. Contains 334827 sequences. (Running on oeis4.)