A157622 31250n - 9100.

22150, 53400, 84650, 115900, 147150, 178400, 209650, 240900, 272150, 303400, 334650, 365900, 397150, 428400, 459650, 490900, 522150, 553400, 584650, 615900, 647150, 678400, 709650, 740900, 772150, 803400, 834650, 865900, 897150, 928400

Offset

1,1

Comments

The identity (781250*n^2-455000*n+66249)^2-(625*n^2-364*n+53)*(31250*n-9100)^2=1 can be written as A157623(n)^2-A157621(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*(22150+9100*x)/(x-1)^2.

Mathematica

LinearRecurrence[{2, -1}, {22150, 53400}, 30]
31250*Range[30]-9100 (* Harvey P. Dale, Nov 16 2018 *)

Prog

(Magma) I:=[22150, 53400]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];
(PARI) a(n) = 31250*n-9100.

Crossrefs

Cf. A157621, A157623.

Sequence in context: A062564 A043590 A043815 * A225392 A225998 A209396

Adjacent sequences: A157619 A157620 A157621 * A157623 A157624 A157625

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 03 2009

Status

approved