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A123116 Values y of solutions (x, y) to the Diophantine equation (x-y)^4-8xy=0 with x>=y. 1
0, 4, 192, 6860, 235008, 7994836, 271656000, 9228697244, 313506312192, 10649999100580, 361786539945408, 12290092806887276, 417501371504448000, 14182756553557856884, 481796221538133532992, 16366888776259793834300, 555992422174307055403008 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Corresponding x-values (A123057) are x(n) = c(n)*(1+d(n)) with c(n) and d(n) defined in formula section.

The pair (x,y) = (A001542(n), a(n)) satisfies the equation 2*x^4 - 2*x*y - y^2 = 0. - Alexander Samokrutov, Sep 04 2015

LINKS

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (40,-206,40,-1).

FORMULA

a(n) = c(n)*(-1+d(n)) with c(0)=0,c(1)=2 and c(n) = 6*c(n-1)-c(n-2) d(0)=1,d(1)=3 and d(n) = 6*d(n-1)-d(n-2).

For n>=4, a(n) = 40*a(n-1) - 206*a(n-2) + 40*a(n-3) - a(n-4). - Max Alekseyev, Nov 13 2009

G.f.: 4*x*(x^2+8*x+1)/((x^2-34*x+1)*(x^2-6*x+1)). - Colin Barker, Oct 25 2012

a(n) = A123057(n) - 2*A001542(n). - Alexander Samokrutov, Sep 05 2015

MATHEMATICA

LinearRecurrence[{40, -206, 40, -1}, {0, 4, 192, 6860}, 40] (* Vincenzo Librandi, Sep 22 2015 *)

PROG

(PARI) concat(0, Vec(4*x*(x^2+8*x+1)/((x^2-34*x+1)*(x^2-6*x+1)) + O(x^20))) \\ Michel Marcus, Sep 05 2015

(MAGMA) I:=[0, 4, 192, 6860]; [n le 4 select I[n] else 40*Self(n-1)-206*Self(n-2)+40*Self(n-3)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Sep 22 2015

CROSSREFS

Cf. A123057.

Sequence in context: A285882 A208184 A172809 * A163839 A012015 A012102

Adjacent sequences:  A123113 A123114 A123115 * A123117 A123118 A123119

KEYWORD

nonn,easy

AUTHOR

Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 28 2006

EXTENSIONS

More terms from Max Alekseyev, Nov 13 2009

Edited by Michel Marcus, Sep 05 2015

STATUS

approved

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Last modified December 10 04:15 EST 2019. Contains 329885 sequences. (Running on oeis4.)