The paper deals with some generalizations of Fibonacci and Lucas sequences, arising from powers of paths and cycles, respectively. In the first part of the work we provide a formula for the number of edges of the Hasse diagram of the independent sets of the h power of a path ordered by inclusion. For h = 1 such a diagram is called a Fibonacci cube, and for h > 1 we obtain a generalization of th...

sharply against the white tile. The space ahead opened into a crosswalk bridging the hospital towers over the street below. Light streamed in through the large glass panels, painting the ground yellow. White coats littered the corridor, and I glanced beyond them at the cars passing underneath. They felt distant and small. Inside the room, Mr. Lucas sat on the bed folding his brother’s clothes. ...

A. Topics and Tools ............................................................................ 1 B. The Lucas Model in Historical Perspective ............................................ 2 Keynesian macroeconomics in the 1960s ......................................................................... 2 Monetarism ....................................................................................

A. Topics and Tools ............................................................................ 1 B. The Lucas Model in Historical Perspective............................................ 2 Keynesian macroeconomics in the 1960s ......................................................................... 2 Monetarism .....................................................................................

In this paper, we define and investigate modified p-Leonardo, p-Leonardo-Lucas p-Leonardo sequences as special cases of the generalized Leonardo sequence. We present Binet's formulas, generating functions, Simson summation formulas for these sequences. Moreover, give some identities matrices related with Furthermore, show that there are close relations between p-Leonardo-Lucas, numbers Fibonacc...

In this paper, a generalization of Lucas addition chains, where subtraction is allowed, is given. It is called ”Lucas addition-subtraction chain” (LASC). LASC gives minimal addition-subtraction chains for infinitely many integers and will also be used to prove the optimality of Lucas addition chains for many cases. One of the main result in the theory of addition-subtraction chains is due to Vo...

The goal of this study is to develop some new connection formulae between two generalized classes Fibonacci and Lucas polynomials. Hypergeometric functions the kind 2F1(z) are included in all coefficients for a specific z. Several famous polynomials, such as Fibonacci, Lucas, Pell, Fermat, Pell–Lucas, Fermat–Lucas deduced special cases derived formulae. Some introduced generalize those existing...

In this paper, the matrices related to Fibonacci, Lucas, Pell, and Pell-Lucas numbers have been examined. By using these new identities integer sequences investigated.