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A081554
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a(n)=sqrt(2)((3+2sqrt(2))^n-(3-2sqrt(2))^n).
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2
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)^2=2*A003499(n)^2-8. a(n)=8*A001109.
Numbers n such that (ceiling(sqrt(n*n/2)))^2 = 4 + n*n/2 [From Ctibor O. Zizka (c.zizka(AT)email.cz), Nov 09 2009]
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
| G.f.: 8x/(1-6x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]
a(0)=0, a(1)=8, a(n)=6*a(n-1)-a(n-2) for n>1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 19 2009]
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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] (* From Harvey P. Dale, Mar 11 2011 *)
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CROSSREFS
| Sequence in context: A026706 A128734 A006321 * A079743 A079765 A079744
Adjacent sequences: A081551 A081552 A081553 * A081555 A081556 A081557
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KEYWORD
| easy,nonn
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Mar 21 2003
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