Bicknell-Johnson, M., and Spears, C.P. Classes of identities for the generalized Fibonacci numbers G_{n} = G_{n-1} + G_{n-c} from matrices with constant valued determinants.

Fibonacci Quarterly 34.3:121-128, 1996.

The generalized Fibonacci numbers {G_{n}}, G_{n} = G_{n-1} + G_{n-c},
n>c,G_{0} = 0,G_{1} = G_{2} = ... = G_{c-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, G_{n}=F_{n}, the n^{th} Fibonacci number, when c-2.
Also, G_{n} = 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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