A072818 Possibly the only integers of the form sqrt(m^2*(m^2-1)*2/3) [only checked for the first 5 terms].

0, 20, 1960, 192060, 18819920, 1844160100, 180708869880, 17707625088140, 1735166549767840, 170028614252160180, 16661069030161929800, 1632614736341616960220, 159979583092448300171760

Offset: 0

Author

Henry Bottomley, Jul 14 2002

Keywords

• nonn

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.

Examples

			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.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..501
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (98, -1).

Formula

a(n) = 98*a(n-1)-a(n-2) [starting with a(0)=0 and a(1)=20] =sqrt(A072819(A001079(n))).

G.f.: 20x/(1-98x+x^2). [Philippe Deléham, Nov 18 2008]