A157857 a(n) = 3600*n^2 - n.

3599, 14398, 32397, 57596, 89995, 129594, 176393, 230392, 291591, 359990, 435589, 518388, 608387, 705586, 809985, 921584, 1040383, 1166382, 1299581, 1439980, 1587579, 1742378, 1904377, 2073576, 2249975, 2433574, 2624373, 2822372

Offset

1,1

Comments

The identity (103680000*n^2 - 28800*n + 1)^2 - (3600*n^2 - n)*(1728000*n - 240)^2 = 1 can be written as A157859(n)^2 - a(n)*A157858(n)^2 = 1 (see second comment at A157858). - Vincenzo Librandi, Jan 25 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: x*(3599 + 3601*x)/(1-x)^3. - Colin Barker, Jan 17 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 25 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {3599, 14398, 32397}, 40] (* Vincenzo Librandi, Jan 25 2012 *)
Table[3600n^2-n, {n, 30}] (* Harvey P. Dale, Apr 13 2019 *)

Prog

(Magma) I:=[3599, 14398, 32397]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 25 2012
(PARI) for(n=1, 30, print1(3600*n^2 - n", ")); \\ Vincenzo Librandi, Jan 25 2012

Crossrefs

Cf. A157858, A157859.

Sequence in context: A186214 A188100 A230023 * A141781 A348627 A216682

Adjacent sequences: A157854 A157855 A157856 * A157858 A157859 A157860

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 08 2009

Status

approved