A157960 a(n) = 121*n^2 - n.

120, 482, 1086, 1932, 3020, 4350, 5922, 7736, 9792, 12090, 14630, 17412, 20436, 23702, 27210, 30960, 34952, 39186, 43662, 48380, 53340, 58542, 63986, 69672, 75600, 81770, 88182, 94836, 101732, 108870, 116250, 123872, 131736, 139842

Offset

1,1

Comments

The identity (242*n - 1)^2 - (121*n^2 - n)*22^2 = 1 can be written as A157961(n)^2 - a(n)*22^2 = 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*(11^2*t-1)).

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

Formula

G.f.: x*(-120 - 122*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}, {120, 482, 1086}, 50] (* Vincenzo Librandi, Feb 10 2012 *)

Prog

(Magma) I:=[120, 482, 1086]; [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 10 2012
(PARI) for(n=1, 40, print1(121*n^2 - n", ")); \\ Vincenzo Librandi, Feb 10 2012

Crossrefs

Cf. A157961.

Sequence in context: A304284 A167562 A033697 * A067915 A305072 A221563

Adjacent sequences: A157957 A157958 A157959 * A157961 A157962 A157963

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 10 2009

Status

approved