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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