A157820 27225n^2 + 2n.

27227, 108904, 245031, 435608, 680635, 980112, 1334039, 1742416, 2205243, 2722520, 3294247, 3920424, 4601051, 5336128, 6125655, 6969632, 7868059, 8820936, 9828263, 10890040, 12006267, 13176944, 14402071, 15681648, 17015675

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 A157822(n)^2-a(n)* A157821(n)^2=1.

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).

G.f.: x*(-27227-27223*x)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {27227, 108904, 245031}, 30]

Prog

(Magma) I:=[27227, 108904, 245031]; [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) = 27225*n^2 + 2*n.

Crossrefs

Cf. A157821, A157822.

Sequence in context: A157814 A216943 A250852 * A251777 A032746 A099230

Adjacent sequences: A157817 A157818 A157819 * A157821 A157822 A157823

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Extensions

Corrected by Charles R Greathouse IV, Aug 09 2010

Status

approved