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pan xhorn (南风)

Works at 自宅

Attended 四川大学

Lives in 北京

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### pan xhorn

Shared publicly -wow

**Pascal's triangle and the number e**

*Pascal's triangle*is a triangular array of integers, the first few rows of which are shown in the picture. Apart from the flanking strips of 1s, each entry is the sum of the two entries above it. There are many well known patterns among the entries of Pascal's triangle. Two of these patterns are (a) that the sum of the entries in the n-th row is equal to 2^n, and (b) that the alternating sum of entries in the n-th row is equal to 0. For example, if n = 4, this means (a) that 1+4+6+4+1 = 2^4 = 16, and (b) that 1-4+6-4+1 = 0.

A less studied sequence associated with Pascal's triangle is the

*product*of the entries in each row. This sequence, which appears as A001142 in

*The On-Line Encyclopedia of Integer Sequences*(http://oeis.org/A001142) begins

1, 1, 2, 9, 96, 2500, 162000, 26471025, ...

Let us denote the entries of this sequence by p(1), p(2), p(3), and so on. The remarkable property of the sequence, illustrated in the picture, is that as n becomes large, the value of p(n-1)p(n+1)/(p(n)^2) converges, albeit slowly, to the number e. The number e, which is approximately 2.718281828459045, is a famous irrational number, and is important because it is the base of the natural logarithm.

This post is based on a post by +Richard Elwes, which you can find here (https://plus.google.com/114216686796425894192/posts/EvZyEiKRJtn). The result itself is due to +Harlan Brothers. +Alexander Bogomolny has written up a nice proof of the result here (http://www.cut-the-knot.org/arithmetic/algebra/HarlanBrothers.shtml).

#mathematics

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### pan xhorn

Shared publicly -Might be handy for some of you: iptables mitigation (using u32 matching) for #heartbleed; logs then drops all TLS heartbeat handshakes.

# Log rules

iptables -t filter -A INPUT -p tcp --dport 443 -m u32 --u32 "52=0x18030000:0x1803FFFF" -j LOG --log-prefix "BLOCKED: HEARTBEAT"

# Block rules

iptables -t filter -A INPUT -p tcp --dport 443 -m u32 --u32 "52=0x18030000:0x1803FFFF" -j DROP

Source: http://www.securityfocus.com/archive/1/531779/30/0/threaded

# Log rules

iptables -t filter -A INPUT -p tcp --dport 443 -m u32 --u32 "52=0x18030000:0x1803FFFF" -j LOG --log-prefix "BLOCKED: HEARTBEAT"

# Block rules

iptables -t filter -A INPUT -p tcp --dport 443 -m u32 --u32 "52=0x18030000:0x1803FFFF" -j DROP

Source: http://www.securityfocus.com/archive/1/531779/30/0/threaded

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### pan xhorn

commented on a video on YouTube.不跪会死啊。。。

哀其不幸,怒其不争

哀其不幸,怒其不争

3

那时候可能真的会死

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死理性派,linux, emacs user,python and qt programmer,learning functional programming

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- 四川大学2003 - 2013
- 中国石油大学2009 - 2012

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xhorn, pronghorn, 南风