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小 發表於 2016-10-19 10:30 PM (第 2718 天)
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You should try and work out what the pattern in the series is. This is how I would go about doing it:
a(4) = a(1+3) = a(1+2) + a(1+1) +a(1) = a(3) + a(2) + a(1)
a(5) = a(4) + a(3) + a(2) = a(3) + a(2) + a(1) + a(3) + a(2) = 2a(3) + 2a(2) + a(1)
a(6) = a(5) + a(4) +a(3) = 2a(3) + 2a(2) + a(1) +a(4) + a(3) = 2a(3) + 2a(2) + a(1) + a(3) + a(2) +
a(1) + a(3) = 3a(3) + 3a(2) + 2a(1)
If you continue to work see what a(7) and a(8) are, you should then be able to work out a general pattern of a(m) = xa(3) + ya(2) + za(1), where m is an integer greater than or equal to 4, and x, y and z are integers.
Hope this helps.