login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A153644 a(n) = 4*n^2 + 28*n + 10. 1

%I

%S 42,82,130,186,250,322,402,490,586,690,802,922,1050,1186,1330,1482,

%T 1642,1810,1986,2170,2362,2562,2770,2986,3210,3442,3682,3930,4186,

%U 4450,4722,5002,5290,5586,5890,6202,6522,6850,7186,7530,7882,8242,8610,8986,9370

%N a(n) = 4*n^2 + 28*n + 10.

%C Sequence gives values of x such that x^3 + 39x^2 = y^2 since a(n)^3 + 39*a(n)^2 = (8n^3 + 84n^2 + 216n + 70)^2.

%C a(n) = 2*(seventh diagonal to A153238).

%C About the first comment, naturally, the complete list of nonnegative values of x in x^3 + 39*x^2 = y^2 is given by x = m^2-39 with m>6. - _Bruno Berselli_, Jan 25 2012

%H Vincenzo Librandi, <a href="/A153644/b153644.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F From _Colin Barker_, Jan 24 2012: (Start)

%F a(1)=42, a(2)=82, a(3)=130, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

%F G.f.: 2*x*((3-x)*(7-5*x))/(1-x)^3. (End)

%F E.g.f.: 2*(-5 + (5 + 16*x + 2*x^2)*exp(x)). - _G. C. Greubel_, Aug 23 2016

%t LinearRecurrence[{3,-3,1},{42,82,130}, 25] (* _G. C. Greubel_, Aug 23 2016 *)

%o (PARI) a(n)=4*n*(n+7)+10 \\ _Charles R Greathouse IV_, Jan 24 2012

%o (MAGMA) [4*n^2 + 28*n + 10: n in [1..50]]; // _Vincenzo Librandi_, Jan 25 2012

%Y Cf. A153238, A067076.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Dec 30 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 11 02:33 EST 2019. Contains 329912 sequences. (Running on oeis4.)