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%I #38 Sep 08 2022 08:46:21
%S 0,20,70,162,308,520,810,1190,1672,2268,2990,3850,4860,6032,7378,8910,
%T 10640,12580,14742,17138,19780,22680,25850,29302,33048,37100,41470,
%U 46170,51212,56608,62370,68510,75040,81972,89318,97090,105300,113960,123082,132678,142760
%N a(n) = 2*n^3 + 9*n^2 + 9*n.
%C y-values solving the Diophantine equation 4*x^3 + 9*x^2 = y^2 for positive x (which are listed in A028552). The equation is also satisfied by y=2 and x=-2.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f.: 2*x*(10 - 5*x + x^2) / (1 - x)^4.
%F a(n) = n*(2*n^2 + 9*n + 9) = n * A014107(n+3).
%t Table[2 n^3 + 9 n^2 + 9 n, {n, 0, 40}] (* or *) CoefficientList[Series[(20 x - 10 x^2 + 2 x^3) / (1 - x)^4, {x, 0, 33}], x]
%o (Magma) [2*n^3+9*n^2+9*n: n in [0..40]]
%o (GAP) List([0..50],n->n*(2*n^2+9*n+9)); # _Muniru A Asiru_, Apr 29 2018
%Y Cf. A014107, A028552 (associated x).
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Apr 28 2018
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