For each integer n ≥ 1, let pn be the number of legal strings with n letters that also read the same right to left as they do left to right (like 'xxxvxxx', for example). Which of the following expressions is equal to P101? OP50 +3P49 Ot50 + 3t48 Ot50 + t48 Ot100 +t99 OP100 + P99 Ot50 + 3t49 P50 + P49 Ot50+ t49

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Call a string of letters "legal" if it can be produced by concatenating (running together) copies of the
following strings:
'v', 'ww', 'xxx' 'yyy' and 'zzz'.
For example, the string 'xxxvv is legal because it can be produced by concatenating 'xxx', 'u' and '
v, but the string 'xxxxv' is not legal.
For each integer n ≥ 1, let t,, be the number of legal strings with n letters. For example, t₁ = 1 (u is
the only the legal string).
t₂ = 2
t3
6
tn = atn-1 + btn-2 + ctn-3 for each integer n 24
b El -36 and c
-
where a =
12
24
Transcribed Image Text:Call a string of letters "legal" if it can be produced by concatenating (running together) copies of the following strings: 'v', 'ww', 'xxx' 'yyy' and 'zzz'. For example, the string 'xxxvv is legal because it can be produced by concatenating 'xxx', 'u' and ' v, but the string 'xxxxv' is not legal. For each integer n ≥ 1, let t,, be the number of legal strings with n letters. For example, t₁ = 1 (u is the only the legal string). t₂ = 2 t3 6 tn = atn-1 + btn-2 + ctn-3 for each integer n 24 b El -36 and c - where a = 12 24
For each integer n ≥ 1, let pn be the number of legal strings with n letters that also read the same
right to left as they do left to right (like 'xxxvxxx', for example).
Which of the following expressions is equal to P101?
OP50 +3P49
Ot50 + 3t48
Ot50 + t48
Ot100 +t99
OP100 + P99
Ot50 + 3t49
Op50 + P49
Ot50+ t49
Transcribed Image Text:For each integer n ≥ 1, let pn be the number of legal strings with n letters that also read the same right to left as they do left to right (like 'xxxvxxx', for example). Which of the following expressions is equal to P101? OP50 +3P49 Ot50 + 3t48 Ot50 + t48 Ot100 +t99 OP100 + P99 Ot50 + 3t49 Op50 + P49 Ot50+ t49
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