A157816 a(n) = 1482401250*n^2 - 108900*n + 1.

1482292351, 5929387201, 13341284551, 23717984401, 37059486751, 53365791601, 72636898951, 94872808801, 120073521151, 148239036001, 179369353351, 213464473201, 250524395551, 290549120401, 333538647751, 379492977601, 428412109951

Offset

1,1

Comments

The identity (1482401250*n^2 - 108900*n + 1)^2 - (27225*n^2 - 2*n)*(8984250*n - 330)^2 = 1 can be written as a(n)^2 - A157814(n)*A157815(n)^2 = 1.

This is the case s=165 and r=1 of the identity (2*(s^2*n-r)^2-1)^2 - (((s^2*n-r)^2-1)/s^2)*(2*s*(s^2*n-r))^2 = 1, where ((s^2*n-r)^2-1)/s^2 is an integer if r^2 == 1 (mod s^2). - Bruno Berselli, Apr 24 2018

Links

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

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

Formula

G.f.: x*(1482292351 + 1482510148*x + x^2)/(1 - x)^3.

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

Mathematica

LinearRecurrence[{3, -3, 1}, {1482292351, 5929387201, 13341284551}, 30]

Prog

(Magma) I:=[1482292351, 5929387201, 13341284551]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..30]];
(PARI) a(n) = 1482401250*n^2 - 108900*n + 1;

Crossrefs

Cf. A157814, A157815.

Sequence in context: A256891 A320873 A166113 * A157822 A034616 A084551

Adjacent sequences: A157813 A157814 A157815 * A157817 A157818 A157819

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Status

approved