A156735 a(n) = 57122*n^2 + 47320*n + 9801.

9801, 114243, 332929, 665859, 1113033, 1674451, 2350113, 3140019, 4044169, 5062563, 6195201, 7442083, 8803209, 10278579, 11868193, 13572051, 15390153, 17322499, 19369089, 21529923, 23805001, 26194323, 28697889, 31315699

Offset: 0

Author

Vincenzo Librandi, Feb 15 2009

Keywords

• nonn
• easy

Comments

The identity (57122*n^2 +47320*n +9801)^2 - (169*n^2 +140*n +29)*(4394*n +1820)^2 = 1 can be written as a(n)^2 - A156640(n)*A156636(n)^2 = 1.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A156636, A156640, A156718.

Programs

Magma

I:=[9801, 114243, 332929]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];

Maple

A156735:= n-> 57122*n^2 + 47320*n + 9801; seq(A156735(n), n=0..50); # G. C. Greubel, Feb 28 2021

Mathematica

LinearRecurrence[{3,-3,1},{9801,114243,332929},50]
CoefficientList[Series[(9801 +84840x +19603x^2)/(1-x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, May 03 2014 *)
Table[57122n^2+47320n+9801,{n,0,30}] (* Harvey P. Dale, Jan 30 2024 *)

PARI

a(n)= 57122*n^2+47320*n+9801 \\ Charles R Greathouse IV, Dec 23 2011

Sage

[57122*n^2 + 47320*n + 9801 for n in (0..50)] # G. C. Greubel, Feb 28 2021

Formula

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) for n>2.

G.f.: (9801 + 84840*x + 19603*x^2)/(1 - x)^3. - Vincenzo Librandi, May 03 2014

E.g.f.: (9801 +104442*x +57122*x^2)*exp(x). - G. C. Greubel, Feb 28 2021

Extensions

Edited by Charles R Greathouse IV, Jul 25 2010