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A158071 64n + 1. 2
65, 129, 193, 257, 321, 385, 449, 513, 577, 641, 705, 769, 833, 897, 961, 1025, 1089, 1153, 1217, 1281, 1345, 1409, 1473, 1537, 1601, 1665, 1729, 1793, 1857, 1921, 1985, 2049, 2113, 2177, 2241, 2305, 2369, 2433, 2497, 2561, 2625, 2689, 2753, 2817, 2881 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (64*n+1)^2-(64*n^2+2*n)*8^2 = 1 can be written as a(n)^2-A158070(n)*8^2 = 1. - Vincenzo Librandi, Feb 11 2012

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*(8^2*t+2)).

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

G.f.: x*(65-x)/(1-x)^2. - Vincenzo Librandi, Feb 11 2012

a(n) = 2*a(n-1)-a(n-2). - Vincenzo Librandi, Feb 11 2012

MATHEMATICA

Range[65, 7000, 64] (* Vladimir Joseph Stephan Orlovsky, Jul 12 2011 *)

LinearRecurrence[{2, -1}, {65, 129}, 50] (* Vincenzo Librandi, Feb 11 2012 °)

PROG

(MAGMA) I:=[65, 129]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 11 2012

(PARI) for(n=1, 50, print1(64*n + 1", ")); \\ Vincenzo Librandi, Feb 11 2012

CROSSREFS

Cf. A158070.

Sequence in context: A118159 A044188 A044569 * A073631 A285300 A194002

Adjacent sequences:  A158068 A158069 A158070 * A158072 A158073 A158074

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 12 2009

STATUS

approved

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Last modified December 11 16:02 EST 2017. Contains 295905 sequences.