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A154022 a(n) = 5*A097780(n-2). 2
0, 5, 125, 3120, 77875, 1943755, 48516000, 1210956245, 30225390125, 754423796880, 18830369531875, 470004814499995, 11731289992968000, 292812245009700005, 7308574835249532125, 182421558636228603120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If a(n)=x and a(n+1)=y, then (x^2+y^2)/(xy+1)=25.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (25,-1).

FORMULA

a(n) = +25*a(n-1) -a(n-2).

a(n) = (5/207)*sqrt(69)*( ((25 + 3*sqrt(69))/2)^(n-1) -((25 - 3*sqrt(69) )/2)^(n-1) ). - Paolo P. Lava, Jan 15 2009

G.f.: 5*x^2/(1 -25*x +x^2). - R. J. Mathar, Jan 05 2011

MATHEMATICA

CoefficientList[Series[(5*z)/(z^2-25*z+1), {z, 0, 25}], z] (* Vincenzo Librandi, Jan 29 2012 *)

LinearRecurrence[{25, -1}, {0, 5}, 20] (* Harvey P. Dale, Mar 06 2018 *)

PROG

(PARI) concat(0, Vec(5/(1-25*x+x^2)+O(x^98))) \\ Charles R Greathouse IV, Dec 27 2011

(Magma) I:=[0, 5]; [n le 2 select I[n] else 25*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jan 29 2012

CROSSREFS

Cf. A065100, A154021-A154027.

Sequence in context: A354654 A067081 A195801 * A013710 A202628 A358110

Adjacent sequences: A154019 A154020 A154021 * A154023 A154024 A154025

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.

STATUS

approved

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)