Re: Lucas 1874 Fibonacci as binomial sum generalization problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg114836] Re: Lucas 1874 Fibonacci as binomial sum generalization problem*From*: Roger Bagula <roger.bagula at gmail.com>*Date*: Sun, 19 Dec 2010 05:10:28 -0500 (EST)*References*: <iecqtn$bjn$1@smc.vnet.net> <iehefr$avr$1@smc.vnet.net>

I made a mistake in the root solve: m71 = {{0, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 1}} CharacteristicPolynomial[m71, x] Table[x /. NSolve[CharacteristicPolynomial[m71, x] == 0, x][[i]], {i, 1, 7}] Abs[%] With that the general polynomial solution appears to be: x^(k+1)-x^k-1; k,1,2,3,... Roger Bagula