A157821 8984250n + 330.

8984580, 17968830, 26953080, 35937330, 44921580, 53905830, 62890080, 71874330, 80858580, 89842830, 98827080, 107811330, 116795580, 125779830, 134764080, 143748330, 152732580, 161716830, 170701080, 179685330, 188669580, 197653830

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-A157820(n)*a(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 (2,-1).

Formula

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

G.f.: x*(8984580-330x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {8984580, 17968830}, 30]

Prog

(Magma) I:=[8984580, 17968830]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..30]];
(PARI) a(n) = 8984250*n + 330.

Crossrefs

Cf. A157820, A157822.

Sequence in context: A234192 A162021 A157815 * A106787 A105012 A186139

Adjacent sequences: A157818 A157819 A157820 * A157822 A157823 A157824

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Status

approved