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A287335 Nonnegative numbers k such that 3*k + 2 is a cube.

%I A287335 #21 Sep 08 2022 08:46:19
%S A287335 2,41,170,443,914,1637,2666,4055,5858,8129,10922,14291,18290,22973,
%T A287335 28394,34607,41666,49625,58538,68459,79442,91541,104810,119303,135074,
%U A287335 152177,170666,190595,212018,234989,259562,285791,313730,343433,374954,408347,443666,480965
%N A287335 Nonnegative numbers k such that 3*k + 2 is a cube.
%C A287335 Corresponding cubes are listed in A016791.
%C A287335 Primes in the sequence: 2, 41, 443, 1637, 22973, 34607, 91541, 234989, ...
%H A287335 Bruno Berselli, <a href="/A287335/b287335.txt">Table of n, a(n) for n = 1..1000</a>
%H A287335 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A287335 O.g.f.: x*(2 + 33*x + 18*x^2 + x^3)/(1 - x)^4.
%F A287335 E.g.f.: 1 - (1 - 3*x - 18*x^2 - 9*x^3)*exp(x).
%F A287335 a(n) = 9*n^3 - 9*n^2 + 3*n - 1.
%F A287335 a(n) = A131476(3*n-1) = A212069(3*n-1).
%t A287335 Table[9 n^3 - 9 n^2 + 3 n - 1, {n, 0, 40}]
%t A287335 LinearRecurrence[{4,-6,4,-1},{2,41,170,443},40] (* _Harvey P. Dale_, Aug 28 2021 *)
%o A287335 (Python) [9*n**3-9*n**2+3*n-1 for n in range(1,40)]
%o A287335 (Sage) [9*n^3-9*n^2+3*n-1 for n in (1..40)]
%o A287335 (Maxima) makelist(9*n^3-9*n^2+3*n-1, n, 1, 40);
%o A287335 (Magma) [9*n^3-9*n^2+3*n-1: n in [1..40]];
%Y A287335 Subsequence of A047292.
%Y A287335 Cf. A016791, A131476, A212069.
%Y A287335 Cf. A244728: nonnegative k such that 3*k is a cube.
%Y A287335 Cf. A121628: nonnegative k such that 3*k + 1 is a cube.
%K A287335 nonn,easy
%O A287335 1,1
%A A287335 _Bruno Berselli_, May 23 2017