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[RecurrenceTable][1] is what you think of as NRSolve. [1]: http://reference.wolfram.com/language/ref/RecurrenceTable.html
Thanks for the tip.     Although from the first example in ref/If the If[] should work, Mathematica seems happier with Piecewise[].    Then I was advised to "rationalize" the decimal fractions in the equations, which in this case was easy to do (e.g....