A157619 31250n - 22150.

9100, 40350, 71600, 102850, 134100, 165350, 196600, 227850, 259100, 290350, 321600, 352850, 384100, 415350, 446600, 477850, 509100, 540350, 571600, 602850, 634100, 665350, 696600, 727850, 759100, 790350, 821600, 852850, 884100, 915350

Offset

1,1

Comments

The identity (781250*n^2-1107500*n+392499)^2-(625*n^2-886*n+314)*(31250*n-22150)^2=1 can be written as A157620(n)^2-A157618(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*(9100+22150*x)/(x-1)^2.

Mathematica

LinearRecurrence[{2, -1}, {9100, 40350}, 30]

Prog

(Magma) I:=[9100, 40350]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];
(PARI) a(n) = 31250*n - 22150.

Crossrefs

Cf. A157618, A157620.

Sequence in context: A234532 A097209 A015298 * A233713 A174983 A184381

Adjacent sequences: A157616 A157617 A157618 * A157620 A157621 A157622

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 03 2009

Status

approved