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It is shown that a combinatorial method based on the principle of inclusion and exclusion (Sieve formula) yields generating functions for the enumeration of integer sequences
(4) As application we use Theorem 1.1 to obtain determinant identities for well-known numbers by specializing to specific sequences { a k}... Hence all that remains of the
We establish several basic properties of the Pfaffian transform, and we use the transfer matrix method to show that the set of sequences with rational generating functions is
Komatsu, On the residue classes of integer sequences satisfying a linear three term recurrence formula, Linear Algebra Appl. Wright, An Introduction to the Theory of Numbers ,
Special cases of the results obtained in previous sections include the generating functions for the numbers of k -ary words according to both t -rises and t -descents, which
We study a family of symmetric third-order recurring sequences with the aid of Riordan arrays and Chebyshev polynomials.. Formulas involving both Chebyshev poly- nomials and
In the present paper, using modular properties of these functions, we have obtained by the unique method the exact formulas for a number of representations of numbers by
The ˆ -algorithm is a general extrapolation procedure for accelerating the convergence of sequences.. Acceleration theorems for two classes of sequences of real numbers
