A157861 a(n) = 3600*n^2 + n.

3601, 14402, 32403, 57604, 90005, 129606, 176407, 230408, 291609, 360010, 435611, 518412, 608413, 705614, 810015, 921616, 1040417, 1166418, 1299619, 1440020, 1587621, 1742422, 1904423, 2073624, 2250025, 2433626, 2624427, 2822428

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 A157863(n)^2 - a(n)*A157862(n)^2 = 1. - 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*(3601 + 3599*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}, {3601, 14402, 32403}, 40] (* Vincenzo Librandi, Jan 25 2012 *)

Prog

(Magma) I:=[3601, 14402, 32403]; [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, 22, print1(3600*n^2 + n", ")); \\ Vincenzo Librandi, Jan 25 2012

Crossrefs

Cf. A157862, A157863.

Sequence in context: A068291 A003838 A296907 * A031558 A045817 A107538

Adjacent sequences: A157858 A157859 A157860 * A157862 A157863 A157864

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 08 2009

Status

approved