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Triangular numbers and Recursive Series

  1. Dec 22, 2004 #1
    In the following two recursive series R_i and X_i, the product, R_i * R_(i-1) always equals the triangular number, X_i * (X_i +1)/2. Also, the the product X_i * X_(i+1)/4 = the triangular number, R_i *(R_i +1)/2. The series R_i is R_0 = 2, R_1 = 3, R_i = 6*R_(i-1) - R_(i-2) - 4, and the series X_i is X_1= 3, X_2 = 8, X_i = 6*X_(i-1) - X_(i-2) - 6. It is remarkable that triangular numbers where the arguments are the terms of one recursive series is formed from products of adjacent terms of the other recursive series and vice versa. Any Comments
  2. jcsd
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