A158398 a(n) = 784n^2 - 2n.

782, 3132, 7050, 12536, 19590, 28212, 38402, 50160, 63486, 78380, 94842, 112872, 132470, 153636, 176370, 200672, 226542, 253980, 282986, 313560, 345702, 379412, 414690, 451536, 489950, 529932, 571482, 614600, 659286, 705540, 753362, 802752

Offset

1,1

Comments

The identity (784*n-1)^2-(784*n^2-2*n)*(28)^2 = 1 can be written as A158399(n)^2-a(n)*(28)^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*(28^2*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*(-782-786*x)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {782, 3132, 7050}, 50]

Prog

(Magma) I:=[782, 3132, 7050]; [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) = 784*n^2 - 2*n.

Crossrefs

Cf. A158399.

Sequence in context: A236888 A006113 A212947 * A003914 A238925 A045074

Adjacent sequences: A158395 A158396 A158397 * A158399 A158400 A158401

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved