A200439 Decimal expansion of constant arising in clubbed binomial approximation for the lightbulb process.

2, 7, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3

Offset: 1

Author

Jonathan Vos Post, Nov 17 2011

Keywords

• nonn
• cons

Comments

In the so-called lightbulb process, on days r = 1, ..., n, out of n lightbulbs, all initially off, exactly r bulbs selected uniformly and independent of the past have their status changed from off to on, or vice versa. With W_n the number of bulbs on at the terminal time n and C_n a suitable clubbed binomial distribution, d_{TV}(W_n,C_n) <= 2.7314 sqrt{n} e^{-(n+1)/3} for all n >= 1.

This is the value of the function g_1(9) after eq (16) of the preprint.

Examples

			2.731313... = 1352/495.
		

Links

• Larry Goldstein, Aihua Xia, Clubbed Binomial Approximation for the Lightbulb Process, arXiv:1111.3984v1 [math.PR], Nov 16, 2011.

Crossrefs

Essentially the same as A176040, A153284 and A010684.

Programs

PARI

1352/495. \\ Charles R Greathouse IV, Nov 29 2011

Extensions

Corrected by R. J. Mathar, Nov 29 2011