A168520 a(n) = 98*a(n-1) - a(n-2); a(1) = 0, a(2) = 10.

0, 10, 980, 96030, 9409960, 922080050, 90354434940, 8853812544070, 867583274883920, 85014307126080090, 8330534515080964900, 816307368170808480110, 79989791546224150085880, 7838183264161795899936130, 768061970096309774043654860, 75262234886174196060378240150

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..503

Index entries for linear recurrences with constant coefficients, signature (98, -1).

Formula

From Colin Barker, Oct 08 2015: (Start)

a(n) = 98*a(n-1) - a(n-2) for n>2.

O.g.f.: 10*x^2 / (x^2-98*x+1). (End)

E.g.f.: exp(49*x)*( (49/(2*sqrt(6)))*sinh(20*sqrt(6)*x) - 10*cosh(20*sqrt(6)*x) ) + 10. - G. C. Greubel, Jul 24 2016

Mathematica

LinearRecurrence[{98, -1}, {0, 10}, 30] (* Harvey P. Dale, Sep 19 2011 *)
CoefficientList[Series[10 x/(x^2 - 98 x + 1), {x, 0, 33}], x] (* Vincenzo Librandi, Oct 13 2015 *)

Prog

(PARI) concat(0, Vec(10*x^2/(x^2-98*x+1) + O(x^30))) \\ Colin Barker, Oct 08 2015
(Magma) I:=[0, 10]; [n le 2 select I[n] else 98*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Oct 13 2015

Crossrefs

Cf. A004189, A000108, A000984, A165293.

Sequence in context: A159869 A006242 A163566 * A200993 A365704 A062033

Adjacent sequences: A168517 A168518 A168519 * A168521 A168522 A168523

Keyword

nonn,easy

Author

Mark Dols, Nov 28 2009

Extensions

a(1)=1 changed to a(1)=10, and data changed accordingly, so sequence is a bisection of A004189- Mark Dols, Feb 01 2010

Changed name to match data and offset, Joerg Arndt, Oct 13 2015

Status

approved