A165220 - OEIS

%I #17 Sep 08 2022 08:45:47

%S 0,91,614,1953,4492,8615,14706,23149,34328,48627,66430,88121,114084,

%T 144703,180362,221445,268336,321419,381078,447697,521660,603351,

%U 693154,791453,898632,1015075,1141166,1277289,1423828,1581167,1749690,1929781

%N Numbers n such that 8*n+1 is a cube.

%C For every even n, n^4+(n/2)^3 is a cube.

%C In effect, a(n) = n*(24*n+3+64*n^2) and 8*a(n)+1 = (8*n+1)^3. [_R. J. Mathar_, Oct 18 2010]

%H Vincenzo Librandi, <a href="/A165220/b165220.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F G.f.: x*(91+250*x+43*x^2)/(1-x)^4. [_Colin Barker_, Jun 15 2012]

%t LinearRecurrence[{4, -6, 4, -1}, {0, 91, 614, 1953}, 100] (* _Vincenzo Librandi_, Apr 06 2013 *)

%o (Magma) I:=[0, 91, 614, 1953]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Apr 06 2013

%Y Cf. A017077.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Sep 08 2009

%E Typo corrected by _Zak Seidov_, Sep 14 2009