A158249 a(n) = 256*n^2 - 2*n.

254, 1020, 2298, 4088, 6390, 9204, 12530, 16368, 20718, 25580, 30954, 36840, 43238, 50148, 57570, 65504, 73950, 82908, 92378, 102360, 112854, 123860, 135378, 147408, 159950, 173004, 186570, 200648, 215238, 230340, 245954, 262080, 278718, 295868

Offset

1,1

Comments

The identity (256*n - 1)^2 - (256*n^2 - 2*n)*16^2 = 1 can be written as A158250(n)^2 - a(n)*16^2 = 1.

Links

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

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*(16^2*t-2)).

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*(254 + 258*x)/(1-x)^3.

E.g.f.: 2*x*(127 + 128*x)*exp(x). - G. C. Greubel, Apr 24 2022

Mathematica

LinearRecurrence[{3, -3, 1}, {254, 1020, 2298}, 50]

Prog

(Magma) I:=[254, 1020, 2298]; [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) = 256*n^2-2*n.
(SageMath) [2*n*(128*n-1) for n in (1..50)] # G. C. Greubel, Apr 24 2022

Crossrefs

Cf. A158250.

Sequence in context: A110827 A062664 A258696 * A366553 A255178 A196738

Adjacent sequences: A158246 A158247 A158248 * A158250 A158251 A158252

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 15 2009

Status

approved