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A132592 X-values of solutions to the equation X*(X + 1) - 8*Y^2 = 0. 26
0, 8, 288, 9800, 332928, 11309768, 384199200, 13051463048, 443365544448, 15061377048200, 511643454094368, 17380816062160328, 590436102659356800, 20057446674355970888, 681362750825443653408, 23146276081390728245000, 786292024016459316676608, 26710782540478226038759688 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (35,-35,1).

FORMULA

a(0)=0, a(1)=8 and a(n) = 34*a(n-1) - a(n-2) + 16.

a(n) = -1/2 + (1/4)*(17-12*sqrt(2))^n + (1/4)*(17+12*sqrt(2))^n, with n >= 0. - Paolo P. Lava, Oct 07 2008

a(n) = (A056771(n) - 1)/2. - Max Alekseyev, Nov 13 2009

a(n) = sinh(2*n*arccosh(sqrt(2))^2) (n=0,1,2,3,...). - Artur Jasinski, Feb 10 2010

G.f.: -8*x*(x+1)/((x-1)*(x^2-34*x+1)). - Colin Barker, Oct 24 2012

a(n) = A055792(n+1)-1 = A001541(n)^2 - 1. - Antti Karttunen, Oct 03 2016

MATHEMATICA

Table[Round[N[Sinh[2 n ArcCosh[Sqrt[2]]]^2, 100]], {n, 0, 20}] (* Artur Jasinski, Feb 10 2010 *)

LinearRecurrence[{35, -35, 1}, {0, 8, 288}, 30] (* Vincenzo Librandi, Dec 24 2018 *)

PROG

(MAGMA) I:=[0, 8, 288]; [n le 3 select I[n] else 35*Self(n-1)-35*Self(n-2)+ Self(n-3): n in [1..30]]; // Vincenzo Librandi, Dec 24 2018

CROSSREFS

Cf. A007654.

Cf. A001541, A058331, A001079, A037270, A055792, A071253, A108741, A132592, A146311, A146312, A146313, A173115, A173116, A173121.

Sequence in context: A187191 A054607 A254408 * A034977 A065141 A190840

Adjacent sequences:  A132589 A132590 A132591 * A132593 A132594 A132595

KEYWORD

nonn,easy

AUTHOR

Mohamed Bouhamida, Nov 14 2007

EXTENSIONS

More terms from Max Alekseyev, Nov 13 2009

STATUS

approved

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Last modified March 29 17:23 EDT 2020. Contains 333116 sequences. (Running on oeis4.)