Bicknell-Johnson, M., and Spears, C.P. Classes of identities for the generalized Fibonacci numbers Gn = Gn-1 + Gn-c from matrices with constant valued determinants.
Fibonacci Quarterly 34.3:121-128, 1996.



The generalized Fibonacci numbers {Gn}, Gn = Gn-1 + Gn-c, n>c,G0 = 0,G1 = G2 = ... = Gc-1= 1, are the sums of elements found on successive diagonals of Pascals triangle written in left- justified form, by beginning in the left-most column and moving up ( c - 1 ) and right 1 throughout the array [1]. Of course, Gn=Fn, the nth Fibonacci number, when c-2. Also, Gn = u(n-l; c-1,1), where u(n; p, q) are the generalized Fibonacci numbers of Harris and Styles [2]. In this paper, elementary matrix operations make simple derivations of entire classes of identities for such generalized Fibonacci numbers, and for the Fibonacci numbers themselves.    


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