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Repair batch-0006 pages from live compare

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	From Discrete mathematics		From Discrete mathematics

	# Let us use a generating function to find a formula for s~~<~~sub~~>~~n~~<~~/sub~~>~~, where s~~<~~sub~~>~~0~~<~~/sub~~>~~ = s~~<~~sub~~>~~1~~<~~/sub~~>~~ = 1, and s~~<~~sub~~>~~n~~<~~/sub~~>~~ = -s~~<~~sub~~>~~n-1~~<~~/sub~~>~~ + 6s~~<~~sub~~>~~n-2~~<~~/sub~~>~~ for n ≥ 2.		# Let us use a generating function to find a formula for s<sub>n</sub>, where s<sub>0</sub> = s<sub>1</sub> = 1, and s<sub>n</sub> = -s<sub>n-1</sub> + 6s<sub>n-2</sub> for n ≥ 2.

	6~8 Give a generating fuction for the sequence {a~~<~~sub~~>~~n~~<~~/sub~~>~~}.		6~8 Give a generating fuction for the sequence {a<sub>n</sub>}.
	# Let a~~<~~sub~~>~~r~~<~~/sub~~>~~ be the number of ways to select r balls from 3 red balls, 2 green balls, and 5 white balls.		# Let a<sub>r</sub> be the number of ways to select r balls from 3 red balls, 2 green balls, and 5 white balls.

	# Let a~~<~~sub~~>~~r~~<~~/sub~~>~~ be the number of ways r cents worth of postage can be placed on a letter using only 5c, 12c, and 25c stamps. The positions of the stamps on the letter do not matter.		# Let a<sub>r</sub> be the number of ways r cents worth of postage can be placed on a letter using only 5c, 12c, and 25c stamps. The positions of the stamps on the letter do not matter.

	# Let a~~<~~sub~~>~~r~~<~~/sub~~>~~ be the number of ways to pay for an item costing r cents with pennies, nickels, and dimes.		# Let a<sub>r</sub> be the number of ways to pay for an item costing r cents with pennies, nickels, and dimes.

	=== Induction ===		=== Induction ===
	# ∑(i=1~k)i*2~~<~~sup~~>~~ i-1 ~~<~~/sup~~>~~ = 2~~<~~sup~~>~~k~~<~~/sup~~>~~ (k-1) + 1. Prove it.		# ∑(i=1~k)i*2<sup> i-1 </sup> = 2<sup>k</sup> (k-1) + 1. Prove it.

	=== Contradixtion ===		=== Contradixtion ===

imported>Unknown at 05:30, 7 February 2021

2021-02-07T05:30:20Z

New page

== 선호 | 민경 ==
=== Generating Function ===
세로가 3 가로가 n(2의 배수)인 상자가 있다. 여기에 크가가 2*1인 레고를 채울려고 한다. 가로가 n일때 빈칸 없이 가득채울수 있는 모양의 개수를 클로즈폼으로 구하시오.(Generating Function으로 구하시오)
원반의 개수가 n인 하노이 타워가 있다(막대는 A, B, C). A막대에 있는 원반을 C로 옴기는데 걸리는 최소횟수를 구하시오(단 A와 B만, B와 C만 이동가능하다.
하노이 타워는 큰 원반이 밑으로만 올수 있는 타워이다.

=== Induction ===
시그마(i=1~n)i*(Hi) = n*(n+1)/2*(Hn) -(n-1)*n/4의 식이 사실임을 증명하라

=== Contradixtion ===

== 전체 ==
=== Generating Function ===
From Concrete Mathematics, Chapter 7. Generating Function

# (Warm up) An eccentric collector of 2 x n domino tilings pays $4 for each vertical domino and $1 for each horizontal domino. How many tiling are worth exactly $m by this criterion? For example, when m = 6 there are three solutions.

# (Warmp up) What is Sigma( Hn / 10^n ) ( n >= 0 )?

# (Basic)Solve the recurrence
G(0) = 1
G(n) = G(n-1) + 2G(n-2) + 3G(n-3) + ... + nG(0), for n > 0

# (Homework exercises) How many spanning trees are in an n-wheel( a graph with n "outer" verices in a cycle, each connected to an (n+1)st "hub" vertex), when n >= 3?

From Discrete mathematics

# Let us use a generating function to find a formula for sn, where s0 = s1 = 1, and sn = -sn-1 + 6sn-2 for n ≥ 2.

6~8 Give a generating fuction for the sequence {an}.
# Let ar be the number of ways to select r balls from 3 red balls, 2 green balls, and 5 white balls.

# Let ar be the number of ways r cents worth of postage can be placed on a letter using only 5c, 12c, and 25c stamps. The positions of the stamps on the letter do not matter.

# Let ar be the number of ways to pay for an item costing r cents with pennies, nickels, and dimes.

=== Induction ===
# ∑(i=1~k)i*2 i-1 = 2k (k-1) + 1. Prove it.

=== Contradixtion ===

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Maintenance script: Repair batch-0006 pages from live compare

imported>Unknown at 05:30, 7 February 2021