A140744 Arises in enumerating iterated point-line configurations.

4, 4, 4, 4, 5, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 22, 26, 30, 36, 43, 52, 63, 77, 95, 119, 151, 193, 249, 326, 433, 583, 795, 1102, 1551, 2220, 3233, 4796, 7254, 11194, 17643, 28432, 46898, 79271, 137464, 244869, 448658, 846699, 1648170, 3314300, 6895838

Offset

1,1

Comments

Lower bound of formula (12) on p. 13. For some constants C1 and C2 the paper proves that C1*a(n) <= the number of points in the n-th stage <= C2*(4^4^n).

Links

Table of n, a(n) for n=1..52.

Joshua Cooper and Mark Walters, Iterated Point-Line Configurations Grow Doubly-Exponentially, arXiv:0807.1549 [math.CO], 2008.

Formula

a(n) = floor(4^(1.0488^n)).

Example

a(50) = 3314300 because 4^(1.0488^50) = 3314300.96.
a(51) = 6895838 because 4^(1.0488^51) = 6895838.31.
a(52) = 14869970 because 4^(1.0488^52) = 14869970.9.

Crossrefs

Sequence in context: A006264 A134994 A138195 * A179414 A361248 A388069

Adjacent sequences: A140741 A140742 A140743 * A140745 A140746 A140747

Keyword

easy,nonn,less

Author

Jonathan Vos Post, Jul 12 2008

Status

approved