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Integer sequences
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#	Item
911	2010 U OF I MOCK PUTNAM EXAM Solutions 1. (a) Given a set with n elements (where n is a positive integer), prove that exactly 2n−1 of its subsets have an odd number of elements. (b) Determine, with proof, the number of Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2010-10-02 21:33:48 Number theory Factorial Equidistributed sequence Limit superior and limit inferior Summation Binomial coefficient Mathematics Integer sequences Combinatorics
912	U OF I MOCK PUTNAM EXAM SEPT. 29, [removed]A sequence a0 , a1 , a2[removed]of real numbers is defined recursively by a0 = 1, an+1 = Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2008-10-01 17:30:30 Number theory Integer sequences Factorial Permutation Mathematics Combinatorics Discrete mathematics
913	U OF I MOCK PUTNAM EXAM SEPT. 29, 2009 Solutions 1. Suppose P (x) is a polynomial with integer coefficients such that none of the values P (1), . . . , P[removed]is divisible by[removed]Prove that P (n) 6= 0 for all integer Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2009-09-30 18:49:41 Combinatorics Factorial Mathematics Integer sequences Number theory
914	2011 U OF I MOCK PUTNAM CONTEST 1. [Variation of A2, Putnam[removed]The sequence of digits[removed][removed] ... is obtained by writing out the natural numbers in order. Let f (n) denote the position of the Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2011-10-02 10:33:09 Integer sequences Calculus Binomial coefficient Factorial Series Mathematical series Binomial series Mixing Mathematics Mathematical analysis Combinatorics
915	On the binary expansion of the odd Catalan numbers Florian Luca Instituto de Matem´aticas Universidad Nacional Aut´onoma de M´exico C.P[removed], Morelia, Michoac´an, M´exico Add to Reading List Source URL: youngp.people.cofc.edu Language: English - Date: 2010-02-17 14:43:11 Combinatorics Number theory Complex analysis Pi Factorial Binomial coefficient Mathematics Mathematical analysis Integer sequences
916	2013 UI FRESHMAN MATH CONTEST September 23, 2013, 5 pm - 7 pm 1. Let {an } be the sequence defined by a0 = 0, a1 = 1, a2 = 2, and an = an−1 + an−2 − an−3 + 1 for n ≥ 3. Find, with proof, a2013[removed]Problem A1, Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2013-09-28 17:14:22 Mathematical notation Summation Mathematical proof Integer sequences Number theory Mathematics Mathematical logic Arithmetic
917	On the number of divisors of n! and of the Fibonacci numbers Florian Luca Instituto de Matem´aticas Universidad Nacional Aut´onoma de M´exico C.P[removed], Morelia, Michoac´an, M´exico Add to Reading List Source URL: youngp.people.cofc.edu Language: English - Date: 2012-01-13 10:24:45 Prime number Divisor function Fibonacci number Divisor Factorial Arithmetic function Quadratic residue Mathematics Number theory Integer sequences
918	Seven Staggering Sequences N. J. A. Sloane Algorithms and Optimization Department AT&T Shannon Lab Florham Park, NJ 07932–0971 Email address: [removed] Add to Reading List Source URL: neilsloane.com Language: English - Date: 2012-01-02 21:20:56 Combinatorics Recurrence relations On-Line Encyclopedia of Integer Sequences Sequence Generating function Collatz conjecture Summation Factorial Binomial coefficient Mathematics Integer sequences Number theory
919	Counting the number of solutions of equations in groups by recurrences Umberto Cerruti Dipartimento di Matematica, Universit`a di Torino Via Carlo Alberto 10, 10123 Torino Italy email:[removed] Add to Reading List Source URL: alpha01.dm.unito.it Language: English - Date: 2007-06-04 11:59:12 Integer sequences Recurrence relation Theory of computation Polynomial Factorial Theorems and definitions in linear algebra Fundamental theorem of algebra Mathematics Algebra Combinatorics
920	The Gift Exchange Problem David Applegate and N. J. A. Sloane(a) , AT&T Shannon Labs, 180 Park Ave., Florham Park, NJ[removed], USA. (a) Add to Reading List Source URL: neilsloane.com Language: English - Date: 2012-01-02 21:20:57 Number theory Orthogonal polynomials Bessel polynomials Summation Factorial Recurrence relation Combinatory logic Stirling number Proof that π is irrational Mathematics Integer sequences Combinatorics

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