A157620 781250n^2 - 1107500n + 392499.

66249, 1302499, 4101249, 8462499, 14386249, 21872499, 30921249, 41532499, 53706249, 67442499, 82741249, 99602499, 118026249, 138012499, 159561249, 182672499, 207346249, 233582499, 261381249, 290742499, 321666249, 354152499

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 a(n)^2-A157618(n)*A157619(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*(-66249-1103752*x-392499*x^2)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {66249, 1302499, 4101249}, 30]
Table[781250n^2-1107500n+392499, {n, 40}] (* Harvey P. Dale, Sep 29 2024 *)

Prog

(Magma) I:=[66249, 1302499, 4101249]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 781250*n^2 - 1107500*n + 392499.

Crossrefs

Cf. A157618, A157619.

Sequence in context: A156424 A092376 A251333 * A174757 A379760 A164129

Adjacent sequences: A157617 A157618 A157619 * A157621 A157622 A157623

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 03 2009

Status

approved