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A145528 Numbers x such that (x+91)^3 - x^3 is a square. 1
455, 728182, 1058842239, 1539555953390, 2238513297452887, 3254796794940610374, 4732472301330350096975, 6881011471337534100457342, 10004985946852473251714944359, 14547242685712024770459428706710 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..316

Index entries for linear recurrences with constant coefficients, signature (1455, -1455, 1).

FORMULA

a(n+2)=1454*a(n+1)-a(n)+66066.

a(n)=-(91/2)+(1001/4)*{[727-44*sqrt(273)]^n+[727+44*sqrt(273)]^n}-(91/6)*sqrt(273)*{[727-44 *sqrt(273)]^n-[727+44*sqrt(273)]^n}, with n>=0. - Paolo P. Lava, Nov 25 2008

a(1)=455, a(2)=728182, a(3)=1058842239, a(n)=1455*a(n-1)-1455*a(n-2)+ a(n-3). - Harvey P. Dale, Jun 22 2011

G.f.: (91*x*(-5-727*x+6*x^2))/(-1+1455*x-1455*x^2+x^3). - Harvey P. Dale, Jun 22 2011

EXAMPLE

a(1)=455 because the first relation is (455+91)^3 - 455^3 = 8281^2.

MAPLE

f:= gfun:-rectoproc({a(n+2)=1454*a(n+1)-a(n)+66066, a(1)=455, a(2)=728182}, a(n), remember):

map(f, [$1..20]); # Robert Israel, Sep 24 2017

MATHEMATICA

LinearRecurrence[{1455, -1455, 1}, {455, 728182, 1058842239}, 20] (* or *) CoefficientList[Series[(91 (-5-727 x+6 x^2))/(-1+1455 x-1455 x^2+x^3), {x, 0, 20}], x] (* Harvey P. Dale, Jun 22 2011 *)

CROSSREFS

Sequence in context: A282232 A061544 A015276 * A203058 A116331 A099650

Adjacent sequences:  A145525 A145526 A145527 * A145529 A145530 A145531

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 12 2008

STATUS

approved

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)