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Matrices Formula for Padovan and Perrin Sequences

, 2013
The Padovan and Perrin numbers have the matrix formula, Qn ⎡ ⎣ 0 3 0 0 1 2 ⎤ ⎦ = ⎡ ⎣ 0 1 0 0 0 1 1 1 0 ⎤ ⎦ n ⎡ ⎣ 0 3 0 0 1 2 ⎤ ⎦ . The matrix product is a 3× 2 matrix that when raised to the nth power give a matrix product whose entries are Padovan and ...
K. Sokhuma, Muban Chom
semanticscholar   +1 more source

Certain Matrices Associated with Balancing and Lucas-balancing Numbers

, 2012
\cdots Balancing numbers $n$ and balancers $r$ are originally defined as the solution of the Diophantine equation $1+2+\cdots+(n-1)=(n+1)+(n+2)+\cdots+(n+r)$.
P. Ray
semanticscholar   +1 more source