Recent content by saubbie

Homework Statement Find a linear homogeneous recurrence relation satisfied by an=2^n+n! Homework Equations The Attempt at a Solution The teacher gave us a hint using generating functions. The generating function for f(x) is f(x)=1+2x+4x^2+8x^3+...+1+x+2x^2+6x^3+24x^4+... The...

Homework Statement If all 52 cards are dealt to four players, what is the probability that at least one player has all the cards of one suit? Homework Equations The Attempt at a Solution This could happen for one of the four suits, so for the first card, there are 52C4...

Homework Statement I have multiple problems, all dealing with Burnside's Theorem, perhaps help on one would help explain the others. How many ways may the faces of a cube be colored using 3 colors, up to symmetry of the cube. And, how many ways may the faces of a dodecahedron be colored...

Homework Statement I have two questions. 1.)There are exactly two nonisomorphic graphs with vertex sequence 3, 3, 3,3, 3, 3, 6. Find them. 2.)Does there exist a connected graph with vertex degrees 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3? If there is, then draw such a...

Sorry. The Catalan numbers are 1,1,2,5,14,42,... given by the formula Cn=(1/(n+1))*2n choose n. With 2n choose n equal to (2n)!/(n!n!). Sorry for the bad form, I don't have any math writing program.

Homework Statement I need to prove two things about the Catalan numbers. The first is that Cn is odd iff n=(2^k)-1 for some positive integer k. The second is that given the matrix A defined by the rule a(i,j)=C(i+j), prove that det A=1. I have not covered determinants in my linear class...

Homework Statement I need to find some huge numbers and don't know how to do it using a computer. Everything that I have tried doesn't work because the numbers are too big. Homework Equations The equations are 1/((1-x)(1-x^2)(1-x^3)) and 1/((1-x)(1-x^3)(1-x^4)) where x=10^30. The...

Homework Statement I am trying to find the number of nonnegative integer solutions to a+2b+4c=10^30. I found a generating function, and need to check the coefficient of 10^30. Homework Equations The generating function is 1/((1-x)(1-x^2)(1-x^4)). I found the PFD, which is...

So for all c, there would be (10^30-4c)/2+1 corresponding to every possible c value, but that would give an infinite number of solutions wouldn't it?

Homework Statement I need to find the number of nonnegative integer solutions to the equation a+2b+4c=10^30 Homework Equations The Attempt at a Solution I was thinking of trying to find perhaps some sort of a multinomial generating function, but am not sure how that will help...

Homework Statement I need to find the number of ways to make change for a dollar using an even number of coins, using only pennies, nickels, dimes, quarters, and fifty cent pieces. Homework Equations I found the generating function for the ways of making change for a dollar...

Homework Statement I have two questions. The first is the generating function for a(n)=5a(n-1) - 6(an-2) where a(0)=0 and a(1)=1. The explicit equation for the sequence is 3^n-2^n. The second one is finding the generating function for the sequence of perfect squares {n^2} for n...

Homework Statement The question is to evaluate the infinite series of the Sum[(((-1)^n)*a(n))/10^n], as n goes from zero to infinity, and a(n) is the recurrence relation a(n)=5a(n-1)-6a(n-2) where a(0)=0, and a(1)=1 Homework Equations I found the explicit equation for a(n)=3^n - 2^n...