A173141 a(n) = 49*n^2 + n.

50, 198, 444, 788, 1230, 1770, 2408, 3144, 3978, 4910, 5940, 7068, 8294, 9618, 11040, 12560, 14178, 15894, 17708, 19620, 21630, 23738, 25944, 28248, 30650, 33150, 35748, 38444, 41238, 44130, 47120, 50208, 53394, 56678, 60060, 63540, 67118, 70794, 74568, 78440, 82410, 86478, 90644, 94908, 99270, 103730, 108288

Offset

1,1

Comments

The identity (98*n+1)^2-(49*n^2+n)*(14)^2 = 1 can be written as A157947(n)^2-a(n)*14^2 = 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*(7^2*t+1)).

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

Formula

G.f.: x*(-50-48*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}, {50, 198, 444}, 50] (* Vincenzo Librandi, Feb 10 2012 *)
Table[49n^2+n, {n, 50}] (* Harvey P. Dale, Aug 22 2015 *)

Prog

(Magma) [ 49*n^2+n: n in [1..50] ];
(PARI) for(n=1, 50, print1(49*n^2 + n", ")); \\ Vincenzo Librandi, Feb 10 2012

Crossrefs

Cf. A157947.

Sequence in context: A244701 A180293 A031692 * A115592 A334808 A273293

Adjacent sequences: A173138 A173139 A173140 * A173142 A173143 A173144

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 22 2010

Status

approved