The sequence of square triangular numbers is defined by No = 0, N = 1, and,...

 

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The sequence of square triangular numbers is defined by No = 0, N = 1, and, Nk34 Nk-1-Nk-2+2 for all k > 2. The first few terms are 0, 1, 36, 1225, 41 616, 1 413 721, 48 024 900, 1 631 432 881,.... Verify that Nk-1 Nk+1 = (Nk-1) for all k > 1. The sequence of square triangular numbers is defined by No = 0, N = 1, and, Nk34 Nk-1-Nk-2+2 for all k > 2. The first few terms are 0, 1, 36, 1225, 41 616, 1 413 721, 48 024 900, 1 631 432 881,.... Verify that Nk-1 Nk+1 = (Nk-1) for all k > 1.