A157859 a(n) = 103680000*n^2 - 28800*n + 1.

103651201, 414662401, 933033601, 1658764801, 2591856001, 3732307201, 5080118401, 6635289601, 8397820801, 10367712001, 12544963201, 14929574401, 17521545601, 20320876801, 23327568001, 26541619201, 29963030401, 33591801601

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 a(n)^2 - A157857(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

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

G.f.: x*(-103651201 - 103708798*x - x^2)/(x-1)^3. - Vincenzo Librandi, Jan 25 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {103651201, 414662401, 933033601}, 40] (* Vincenzo Librandi, Jan 25 2012 *)

Prog

(Magma) I:=[103651201, 414662401, 933033601]; [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(103680000*n^2 - 28800*n + 1", ")); \\ Vincenzo Librandi, Jan 25 2012

Crossrefs

Cf. A157857, A157858.

Sequence in context: A241792 A112717 A114679 * A157863 A176773 A035498

Adjacent sequences: A157856 A157857 A157858 * A157860 A157861 A157862

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 08 2009

Status

approved