5. name 数列的精简准确定义; (1)a(n)有无需使用其他未知数的定义;e.g. a(n) = a(n-1) + a(n-3); (2)a(n)的定义需要引入其他参数,一般单参数使用k;e.g. Numbers k such that k and k+1 have the same number of divisors. a(n) is the least nonnegative integer k such that the 2-valuation of 3^k+5 is n, or -1 if no such number exists. *(3)a(n)是数组中的某项;e.g. Largest elements of triples (a, b, c) with a > b > c > 0 such that ab+c, ac+b and bc+a are perfect squares. *(4)a(n)为分数数列的分子或分母;e.g. Numerators of harmonic numbers H(n) = Sum_{i=1..n} 1/i. .
*(5)数列为正方形(准确地说,任一行的项数不确定或无限大):此时data按照副对角线读取; 如 1 2 3 4 … 2 4 6 8 … 4 8 12 16 … 8 16 24 32… … 为1, 2, 2, 4, 4, 3, 8, 8, 6, 4, … name需要由"Table read by antidiagonals: T(n, k) is"开头,T(n, k)表示表格的第n行第k列; e.g. Table read by antidiagonals: T(n,k) is the number of tilings of the n X k torus up to 180-degree rotation by two tiles that are both fixed under 180-degree rotation. *(6)数列为三角形;即前若干行的项数有限。data此时逐行读取即可。 name由"(Irregular) Triangle read by rows: T(n, k) is"开头,若三角形每行项数不是等差数列则为Irregular,T(n, k)表示第n行第k项。