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

1,1

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.

Links

Table of n, a(n) for n=1..75.

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

Example

2.731313... = 1352/495.

Prog

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

Crossrefs

Sequence in context: A110987 A199740 A229952 * A356381 A197281 A019703

Adjacent sequences: A200436 A200437 A200438 * A200440 A200441 A200442

Keyword

nonn,cons

Author

Jonathan Vos Post, Nov 17 2011

Extensions

Corrected by R. J. Mathar, Nov 29 2011

Status

approved