A157863 a(n) = 103680000*n^2 + 28800*n + 1.

103708801, 414777601, 933206401, 1658995201, 2592144001, 3732652801, 5080521601, 6635750401, 8398339201, 10368288001, 12545596801, 14930265601, 17522294401, 20321683201, 23328432001, 26542540801, 29964009601, 33592838401

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 - A157861(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

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

G.f.: x*(-x^2 - 103651198*x - 103708801)/(x-1)^3. - Vincenzo Librandi, Jan 25 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {103708801, 414777601, 933206401}, 40] (* Vincenzo Librandi, Jan 25 2012 *)
Table[103680000*n^2+28800*n+1, {n, 20}] (* Harvey P. Dale, May 27 2020 *)

Prog

(Magma) I:=[103708801, 414777601, 933206401]; [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. A157861, A157862.

Sequence in context: A112717 A114679 A157859 * A176773 A035498 A018897

Adjacent sequences: A157860 A157861 A157862 * A157864 A157865 A157866

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 08 2009

Status

approved