Combinatorial interpretation of generalized Pell numbers. (English) Zbl 1447.11023
Summary: In this note we give combinatorial interpretations for the generalized Pell sequence of order \(k\) by means of lattice paths and generalized bi-colored compositions. We also derive some basic relations and identities by using Riordan arrays.
MSC:
| 11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |
| 05A19 | Combinatorial identities, bijective combinatorics |
Software:
OEISOnline Encyclopedia of Integer Sequences:
Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.Pell numbers: a(0) = 0, a(1) = 1; for n > 1, a(n) = 2*a(n-1) + a(n-2).
Triangle whose (i,j)-th entry is binomial(i,j)*2^(i-j).
Expansion of 1/(1 - 2*x - x^2 - x^3).
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