A157740 a(n) = 18522*n + 42.

18564, 37086, 55608, 74130, 92652, 111174, 129696, 148218, 166740, 185262, 203784, 222306, 240828, 259350, 277872, 296394, 314916, 333438, 351960, 370482, 389004, 407526, 426048, 444570, 463092, 481614, 500136, 518658, 537180, 555702

Offset

1,1

Comments

The identity (388962n^2+1764n+1)^2-(441n^2+2n)*(18522n+42)^2=1 can be written as A157741(n)^2-A158321(n)*a(n)^2=1 (see the second comment in A157741). - Vincenzo Librandi, Feb 05 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

Formula

G.f.: x*(18564-42*x)/(1-x)^2. - Vincenzo Librandi, Feb 05 2012

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

Maple

A157740:=n->18522*n + 42; seq(A157740(n), n=1..50); # Wesley Ivan Hurt, Mar 04 2014

Mathematica

LinearRecurrence[{2, -1}, {18564, 37086}, 50] (* Vincenzo Librandi, Feb 05 2012 *)
18522*Range[30]+42 (* Harvey P. Dale, Apr 02 2023 *)

Prog

(Magma) I:=[18564, 37086]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 05 2012
(PARI) for(n=1, 40, print1(18522n + 42", ")); \\ Vincenzo Librandi, Feb 05 2012

Crossrefs

Cf. A157741, A158321.

Sequence in context: A031817 A236816 A229076 * A248488 A237700 A248065

Adjacent sequences: A157737 A157738 A157739 * A157741 A157742 A157743

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 05 2009

Status

approved