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A072818
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Possibly the only integers of the form sqrt(m^2*(m^2-1)*2/3) [only checked for the first 5 terms].
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1
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0, 20, 1960, 192060, 18819920, 1844160100, 180708869880, 17707625088140, 1735166549767840, 170028614252160180, 16661069030161929800, 1632614736341616960220, 159979583092448300171760
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| These are the standard deviations of time for a random walk starting at 0 to reach one of the boundaries at +A001079(n) or -A001079(n) for the first time.
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LINKS
| Tanya Khovanova, Recursive Sequences
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FORMULA
| a(n) = 98*a(n-1)-a(n-2) [starting with a(0)=0 and a(1)=20] =sqrt(A072819(A001079(n))).
a(n)=(1/12)*[49+20*sqrt(6)]^n*sqrt(6)-(1/12)*sqrt(6)*[49-20*sqrt(6)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Oct 06 2008]
G.f.: 20x/(1-98x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
| 0 and 20 are at the start of the sequence since m^2*(m^2-1)*2/3 (A072819) starts 0, 0, 8, 48, 160, 400, 840, 1568, ... and the only squares among these are 0 and 400 with square roots of 0 and 20.
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CROSSREFS
| Sequence in context: A177297 A014606 A172556 * A123479 A071152 A195622
Adjacent sequences: A072815 A072816 A072817 * A072819 A072820 A072821
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jul 14 2002
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