Netted matrices

Pantelimon Stănică

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-12

Abstract:

We prove that powers of 4 -netted matrices (the entries satisfy a four-term recurrence δ a i , j = α a i − 1 , j + β a i − 1 , j + γ a i , j − 1 ) preserve the property of nettedness: the entries of the e th power satisfy δ e a i , j ( e ) = α e a i − 1 , j ( e ) + β e a i − 1 , j − 1 ( e ) + γ e a i , j − 1 ( e ) , where the coefficients are all instances of the same sequence x e + 1 = ( β + δ ) x e − ( β δ + α γ ) x e − 1 . Also, we find a matrix Q n ( a , b ) and a vector v such that Q n ( a , b ) e ⋅ v acts as a shifting on the general second-order recurrence sequence with parameters a , b . The shifting action of Q n ( a , b ) generalizes the known property ( 0 1 1 1 ) e ⋅ ( 1 , 0 ) t = ( F e − 1 , F e ) t . Finally, we prove some results about congruences satisfied by the matrix Q n ( a , b ) .

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:594182

DOI: 10.1155/S0161171203201071

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