A Study on Generalized Tetranacci Numbers: Closed Form Formulas ∑n k=0 xkWk2 of Sums of the Squares of Terms
Y¨uksel Soykan *
Department of Mathematics, Art and Science Faculty, Zonguldak B¨ulent Ecevit University, 67100, Zonguldak, Turkey
*Author to whom correspondence should be addressed.
Abstract
In this paper, closed forms of the sum formulas ∑n k=0 xkWk2 for the squares of generalized Tetranacci numbers are presented. We also present the sum formulas ∑n k=0 xkWk+1Wk; ∑n k=0 xkWk+2Wk; and ∑n k=0 xkWk+3Wk: As special cases, we give summation formulas of the of Tetranacci, Tetranacci-Lucas and some other fourth order linear recurrance sequences.
Keywords: Sum of squares, fourth order recurrence, Tetranacci numbers, Tetranacci-Lucas numbers.