A157923 a(n) = 49*n^2 - n.

48, 194, 438, 780, 1220, 1758, 2394, 3128, 3960, 4890, 5918, 7044, 8268, 9590, 11010, 12528, 14144, 15858, 17670, 19580, 21588, 23694, 25898, 28200, 30600, 33098, 35694, 38388, 41180, 44070, 47058, 50144, 53328, 56610, 59990, 63468, 67044

Offset

1,1

Comments

The identity (98n - 1)^2 - (49n^2 - n)*14^2 = 1 can be written as A157924(n)^2 - a(n)*14^2 = 1. - Vincenzo Librandi, Feb 05 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*(-48-50*x)/(x-1)^3. - Vincenzo Librandi, Feb 05 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 05 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {48, 194, 438}, 50] (* Vincenzo Librandi, Feb 05 2012 *)

Prog

(Magma) I:=[48, 194, 438]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 05 2012
(PARI) for(n=1, 40, print1(49*n^2 - n", ")); \\ Vincenzo Librandi, Feb 05 2012

Crossrefs

Cf. A157924.

Sequence in context: A259038 A231174 A259245 * A296367 A275507 A072254

Adjacent sequences: A157920 A157921 A157922 * A157924 A157925 A157926

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 09 2009

Status

approved