A154024 a(n+2) = 49*a(n+1) - a(n), a(1)=0, a(2)=7.

0, 7, 343, 16800, 822857, 40303193, 1974033600, 96687343207, 4735705783543, 231952896050400, 11360956200686057, 556454900937566393, 27254929189740067200, 1334935075396325726407

Offset

1,2

Comments

If a(n)=x and a(n+1)=y, then (x^2+y^2)/(xy+1)=49.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..600

Index entries for linear recurrences with constant coefficients, signature (49,-1).

Formula

G.f.: 7*x^2/(1 -49*x +x^2). - R. J. Mathar, Jan 05 2011

Mathematica

LinearRecurrence[{49, -1}, {0, 7}, 30] (* Vincenzo Librandi, Feb 25 2012 *)
Rest@ CoefficientList[Series[7 x^2/(1 - 49 x + x^2), {x, 0, 14}], x] (* Michael De Vlieger, Sep 01 2016 *)

Prog

(PARI) concat(0, Vec(7/(1-49*x+x^2)+O(x^98))) \\ Charles R Greathouse IV, Dec 27 2011
(Magma) I:=[0, 7]; [n le 2 select I[n] else 49*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 25 2012

Crossrefs

Cf. A065100, A154021-A154027.

Sequence in context: A195803 A263220 A145252 * A013712 A109493 A193614

Adjacent sequences: A154021 A154022 A154023 * A154025 A154026 A154027

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 04 2009

Status

approved