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A081554 a(n) = sqrt(2)*( (3+2*sqrt(2))^n - (3-2*sqrt(2))^n ). 2
0, 8, 48, 280, 1632, 9512, 55440, 323128, 1883328, 10976840, 63977712, 372889432, 2173358880, 12667263848, 73830224208, 430314081400, 2508054264192, 14618011503752, 85200014758320, 496582077046168, 2894292447518688 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Numbers m such that ceiling( sqrt(m*m/2) )^2 = 4 + m*m/2. - Ctibor O. Zizka, Nov 09 2009

Numbers m such that 2*m^2+16 is a square. - Bruno Berselli, Dec 17 2014

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (6,-1).

FORMULA

a(n)^2 = 2*A003499(n)^2 - 8.

a(n) = 8*A001109(n).

G.f.: 8*x/(1-6*x+x^2). - Philippe Deléham, Nov 17 2008

a(0)=0, a(1)=8, a(n) = 6*a(n-1) - a(n-2) for n>1. - Philippe Deléham, Sep 19 2009

a(n) = 4*Pell(2*n) = 4*A000129(2*n). - G. C. Greubel, Aug 16 2018

MATHEMATICA

a = 3 + 2Sqrt[2]; b = 3 - 2Sqrt[2]; Table[Simplify[Sqrt[2](a^n - b^n)], {n, 0, 25}]

CoefficientList[Series[8x/(1-6x+x^2), {x, 0, 40}], x]  (* Harvey P. Dale, Mar 11 2011 *)

Table[4 Fibonacci[2 n, 2], {n, 0, 50}] (* G. C. Greubel, Aug 16 2018 *)

PROG

(PARI) x='x+O('x^50); concat([0], Vec(8*x/(1-6*x+x^2))) \\ G. C. Greubel, Aug 16 2018

(MAGMA) m:=50; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(8*x/(1-6*x+x^2))); // G. C. Greubel, Aug 16 2018

CROSSREFS

Sequence in context: A006321 A295047 A295375 * A231109 A079743 A079765

Adjacent sequences:  A081551 A081552 A081553 * A081555 A081556 A081557

KEYWORD

nonn,easy,changed

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Mar 21 2003

STATUS

approved

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Last modified August 18 09:47 EDT 2018. Contains 313826 sequences. (Running on oeis4.)