A193608 - OEIS

%I #26 Sep 08 2022 08:45:58

%S 15,52,125,246,427,680,1017,1450,1991,2652,3445,4382,5475,6736,8177,

%T 9810,11647,13700,15981,18502,21275,24312,27625,31226,35127,39340,

%U 43877,48750,53971,59552,65505,71842,78575,85716,93277,101270,109707,118600

%N The consecutive squares of numbers multiplied by their next consecutive integer.

%H Vincenzo Librandi, <a href="/A193608/b193608.txt">Table of n, a(n) for n = 1..10000</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) = (n+2)*(n^2 + (n+1)^2).

%F G.f.: x*(3-x)*(5-x+2*x^2)/(1-x)^4. [_Colin Barker_, Mar 28 2012]

%t Table[2*(n + 1)^3 - n, {n, 38}] (* _L. Edson Jeffery_, Jan 11 2018 *)

%t LinearRecurrence[{4,-6,4,-1},{15,52,125,246},40] (* _Harvey P. Dale_, May 01 2022 *)

%o (C)

%o int a(int n)

%o {

%o     return ((n+2)*((n*n)*((n+1)*(n+1))));

%o }

%o (PARI) a(n)=2*n^3+6*n^2+5*n+2 \\ _Charles R Greathouse IV_, Jul 31 2011

%o (Magma) [(n+2)*(n^2 + (n+1)^2): n in [1..40] ]; // _Vincenzo Librandi_, Aug 01 2011

%K nonn,easy

%O 1,1

%A _Ankur Trapasiya_, Jul 31 2011