|
%I #20 Sep 08 2022 08:45:27
%S 0,21,114,333,732,1365,2286,3549,5208,7317,9930,13101,16884,21333,
%T 26502,32445,39216,46869,55458,65037,75660,87381,100254,114333,129672,
%U 146325,164346,183789,204708,227157,251190,276861,304224,333333,364242,397005
%N Nonnegative k such that 3*k + 1 is a perfect cube.
%C Intersection of this sequence and A001082 is {0, 21, 1365, 87381,...} all of the form (2^(6*m)-1)/3.
%H Vincenzo Librandi, <a href="/A121628/b121628.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 3*(n - 1)*(3*n^2 - 3*n + 1) with n>0. Corresponding cubes are 3*a(n) + 1 = (3*n - 2)^3.
%F G.f.: 3*x^2*(7 + 10*x + x^2)/(1-x)^4. - _Colin Barker_, Apr 11 2012
%t CoefficientList[Series[3 (7 + 10 x + x^2)/(1 - x)^4, {x, 0, 40}], x] (* _Vincenzo Librandi_, Apr 11 2012 *)
%t LinearRecurrence[{4,-6,4,-1},{0,21,114,333},40] (* _Harvey P. Dale_, Mar 08 2018 *)
%o (Magma) [3*n*(1+3*n+3*n^2): n in [1..40]]; // _Vincenzo Librandi_, Apr 11 2012
%Y Cf. A001082: 3*m + 1 is a perfect square.
%Y Cf. A287335 (see Crossrefs).
%K nonn,easy
%O 1,2
%A _Zak Seidov_, Aug 12 2006
%E 0 added and b-file updated by _Bruno Berselli_, May 23 2017
|
