The federal Pell Grant Program provides billions of dollars in subsidies to low-income college students to increase affordability and access to higher education. I estimate the economic incidence of these subsidies using regression discontinuity (RD) and regression kink (RK) designs. RK estimates suggest that schools capture Pell Grant aid through price discrimination, while RD estimates imply ...

(1) wn+2 = pwn+1 + qwn, with given w0 = a,w1 = b and n ≥ 0. This sequence was introduced, in 1965, by Horadam [Ho], and it generalizes many sequences (see [HW, HM]). Examples of such sequences are Fibonacci numbers sequence (Fn)n≥0, Lucas numbers sequence (Ln)n≥0, and Pell numbers sequence (Pn)n≥0, when one has p = q = b = 1, a = 0; p = q = b = 1, a = 2; and p = 2, q = b = 1, a = 0; respectivel...

In this paper we give a new generalization of the Pell numbers in matrix representation. Also we extend the matrix representation and we show that the sums of the generalized order-k Pell numbers could be derived directly using this representation. Further we present some identities, the generalized Binet formula and combinatorial representation of the generalized order-k Pell numbers.

We introduce a function on sequences, which we call the Pfaffian transform, using the Pfaffian of a skew-symmetric matrix. 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 closed under the Pfaffian transform. We conclude by computing the Pfaffian transform of a variety o...

In this paper we present some identities involving terms of k-Pell, k-Pell-Lucas and Modified k-Pell sequences. We also give some results on the column and row norms of Hankel matrices which entries are numbers of these sequences. Mathematics Subject Classification: 11B37, 11B83, 15A60

In this paper, we introduce and investigate the generalized Olivier sequences deal with, in detail, two special cases, namely, Olivier-Lucas sequences. We present Binet's formulas, generating functions, Simson summation formulas for these also provide variousmatrices identities associated with Furthermore, show that there are close relations between Olivier, adjusted Pell-Padovan, third order L...

The demand for data security schemes has increased with the significant advancement in field of computation and communication networks. We propose a novel three-step text encryption scheme that provable against attacks such as key attack statistical attack. proposed is based on Pell sequence elliptic curves, where at first step plain diffused to get meaningless by applying cyclic shift symbol s...

Generalizations of Binet’s theorem are used to produce generalized Pell sequences from two families of silver means. These Pell sequences are also generated from the family of Fibonacci polynomials. A family of Pell-Lucas sequences are also generated from the family of Lucas polynomials and from another generalization of Binet’s formula. A periodic set of cyclic constants are generated from the...