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A132584 a(0)=0, a(1)=4; for n > 1, a(n) = 18*a(n-1) - a(n-2) + 8. 5
0, 4, 80, 1444, 25920, 465124, 8346320, 149768644, 2687489280, 48225038404, 865363202000, 15528312597604, 278644263554880, 5000068431390244, 89722587501469520, 1610006506595061124, 28890394531209630720, 518417095055178291844, 9302617316461999622480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The old definition given for this sequence was "Sequence allows us to find X values of the equation: X(X + 1) - 5*Y^2 = 0".

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (19,-19,1).

FORMULA

a(n) = -1/2 + (1/4)*(9-4*sqrt(5))^n + (1/4)*(9+4*sqrt(5))^n. - Paolo P. Lava, Oct 07 2008

a(n) = (A023039(n) - 1)/2. - Max Alekseyev, Nov 13 2009

G.f.: -4*x*(x+1)/((x-1)*(x^2-18*x+1)). - Colin Barker, Oct 24 2012

From Amiram Eldar, Jan 11 2022: (Start)

a(n) = 5*Fibonacci(3*n)^2/4 - 1 if n is odd and 5*Fibonacci(3*n)^2/4 if n is even.

A000217(a(n)) = A292443(n). (End)

MATHEMATICA

LinearRecurrence[{19, -19, 1}, {0, 4, 80}, 40] (* Vincenzo Librandi, Dec 24 2018 *)

PROG

(MAGMA) I:=[0, 4, 80]; [n le 3 select I[n] else 18*Self(n-1)-Self(n-2)+8: n in [1..30]]; // Vincenzo Librandi, Dec 24 2018

CROSSREFS

Cf. A000045, A000217, A007654, A023039, A292443.

Sequence in context: A054322 A114488 A055787 * A277074 A012127 A189791

Adjacent sequences:  A132581 A132582 A132583 * A132585 A132586 A132587

KEYWORD

nonn,easy

AUTHOR

Mohamed Bouhamida, Nov 14 2007

EXTENSIONS

More terms from Max Alekseyev, Nov 13 2009

New definition by Antti Karttunen, Oct 24 2012

STATUS

approved

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Last modified August 9 12:53 EDT 2022. Contains 356026 sequences. (Running on oeis4.)