Abstract
We consider an infinite lower triangular matrix L = [ ℓ n , k ] n , k ∈ N 0 and a sequence Ω = ( ω n ) n ∈ N 0 called the ( a,b)-sequence such that every element ℓ n + 1 , k + 1 except lying in column 0 can be expressed as ℓ n + 1 , k + 1 = ∑ i = 0 ⌊ ( n - k ) / m ⌋ ω i ℓ n - ai , k + bi , ω 0 ∉ 0 where a and b are integers with a + b = m > 0 and b ⩾ 0 . This concept generalizes the A-sequence of a Riordan matrix. As a result, we explore several structural properties of Riordan matrices by means of ( a,b)-sequences. In particular, if b < 0 then this leads to an extended Riordan matrix which is a bilaterally infinite matrix.
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