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In this paper, closed forms of the sum formulas ∑n k=0 x W 2 k for the squares of generalized Tetranacci numbers are presented. We also present the sum formulas ∑n k=0 x Wk+1Wk, ∑n k=0 x Wk+2Wk, and ∑n k=0 x Wk+3Wk. As special cases, we give summation formulas of the of Tetranacci, Tetranacci-Lucas and some other fourth order linear recurrance sequences.

A Study on Generalized Tetranacci Numbers: Closed Form Formulas ∑n k=0 xkWk2 of Sums of the Squares of Terms