MathDB

i+a for i = 1, 2, 3, ..., k$ is even for set {a_i}

Source: 1992 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p4

November 20, 2022

combinatorics

Problem Statement

A finite set

\{a_1, a_2, ... a_k\}

of positive integers with

a_1 < a_2 < a_3 < ... < a_k

is named alternating if

i+a

for

i = 1, 2, 3, ..., k

is even. The empty set is also considered to be alternating. The number of alternating subsets of

\{1, 2, 3,..., n\}

is denoted by

A(n)

. Develop a method to determine

A(n)

for every

n \in N

and calculate hence

A(33)