A158316 - OEIS

A158316

a(n) = 400*n^2 - 2*n.

398, 1596, 3594, 6392, 9990, 14388, 19586, 25584, 32382, 39980, 48378, 57576, 67574, 78372, 89970, 102368, 115566, 129564, 144362, 159960, 176358, 193556, 211554, 230352, 249950, 270348, 291546, 313544, 336342, 359940, 384338, 409536

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OFFSET

1,1

COMMENTS

The identity (400*n-1)^2-(400*n^2-2*n)*(20)^2=1 can be written as A158317(n)^2-a(n)*(20)^2=1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(20^2*t-2)).

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*(-398-402*x)/(x-1)^3.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {398, 1596, 3594}, 50]

PROG

(Magma) I:=[398, 1596, 3594]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];

(PARI) a(n) = 400*n^2 - 2*n

CROSSREFS

Cf. A158317.

Sequence in context: A340419 A376801 A191942 * A236713 A235958 A187515