A154023 a(n+2) = 36*a(n+1) - a(n), a(1)=0, a(2)=6.

0, 6, 216, 7770, 279504, 10054374, 361677960, 13010352186, 468011000736, 16835385674310, 605605873274424, 21784976052204954, 783653532006103920, 28189742176167536166, 1014047064810025198056, 36477504590984739593850

Offset

1,2

Comments

If a(n)=x and a(n+1)=y then (x^2+y^2)/(xy+1)=36.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (36,-1).

Formula

From R. J. Mathar, Oct 18 2010: (Start)

a(n)= +36*a(n-1) -a(n-2)

a(n) = 6*A144128(n-1).

G.f.: 6*x/(1 -36*x +x^2). (End)

Mathematica

LinearRecurrence[{36, -1}, {0, 6}, 50] (* Vincenzo Librandi, Jan 30 2012 *)

Prog

(PARI) concat(0, Vec(6/(1-36*x+x^2)+O(x^98))) \\ Charles R Greathouse IV, Dec 27 2011

Crossrefs

Cf. A065100, A154021-A154027.

Sequence in context: A007221 A195802 A145249 * A013711 A300593 A281431

Adjacent sequences: A154020 A154021 A154022 * A154024 A154025 A154026

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 04 2009

Extensions

Edited by N. J. A. Sloane, Jun 23 2010 at the suggestion of Joerg Arndt.

Missing digit inserted in a(8) by R. J. Mathar, Oct 18 2010

Status

approved