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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

Table of n, a(n) for n=0..20.

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]

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 *)

CROSSREFS

Sequence in context: A128734 A006321 A295047 * A231109 A079743 A079765

Adjacent sequences:  A081551 A081552 A081553 * A081555 A081556 A081557

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified November 18 05:25 EST 2017. Contains 294853 sequences.