A173275 - OEIS

A173275

a(n) = 169*n^2 + n.

170, 678, 1524, 2708, 4230, 6090, 8288, 10824, 13698, 16910, 20460, 24348, 28574, 33138, 38040, 43280, 48858, 54774, 61028, 67620, 74550, 81818, 89424, 97368, 105650, 114270, 123228, 132524, 142158, 152130, 162440, 173088, 184074, 195398, 207060, 219060, 231398, 244074, 257088, 270440, 284130, 298158, 312524

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OFFSET

1,1

COMMENTS

The identity (338*n + 1)^2 - (169*n^2 + n)*26^2 = 1 can be written as A158000(n)^2 - a(n)*26^2 = 1. - Vincenzo Librandi, Feb 10 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 14 in the first table at p. 85, case d(t) = t*(13^2*t+1)).

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: x*(-170 - 168*x)/(x-1)^3. - Vincenzo Librandi, Feb 10 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 10 2012

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {170, 678, 1524}, 50] (* Vincenzo Librandi, Feb 10 2012 *)

PROG

(Magma)[169*n^2+n: n in [1..50]]

(PARI) for(n=1, 50, print1(169*n^2+n ", ")); \\ Vincenzo Librandi, Feb 10 2012

CROSSREFS

Cf. A031704, A158000.

Sequence in context: A045089 A114078 A031704 * A301867 A281397 A206122