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A114034
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Let f(n) be the number of sequences of 1's and 2's which sum to n. Sequence contains the string of sequences.
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0
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1, 2, 11, 12, 21, 111, 22, 112, 121, 211, 1111, 122, 212, 221, 1112, 1121, 1211, 2111, 11111, 222, 1122, 1212, 1221, 2112, 2121, 2211, 11112, 11121, 11211, 12111, 21111, 111111, 1222, 2122, 2212, 2221, 11122, 11212, 11221, 12112, 12121, 12211, 21112, 21121, 21211, 22111, 111112, 111121, 111211, 112111, 112111, 121111, 211111, 1111111
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Number of sequences of ones and twos that sum to n are Fibonacci(n+1). The maximum number of terms in a sequence is n. (111111 n times). Following is the triangle of the frequency of sequences of each size:
1
1 1
0 2 1
0 1 3 1
0 0 3 4 1
0 0 1 6 5 1
...
This is a vertical Pascal's triangle and the horizontal sum gives the Fibonacci numbers.
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EXAMPLE
| 1: 1: f(1) = 1.
2: 2,11: f(2) = 2.
3: 12,21,111: f(3) = 3.
4: 22,112,121,211,1111: f(4) = 5.
5: 122,212,221,1112,1121,1211,2111,11111: f(5) = 8.
...
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CROSSREFS
| Sequence in context: A063112 A038113 A089600 * A136970 A136967 A137001
Adjacent sequences: A114031 A114032 A114033 * A114035 A114036 A114037
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 13 2005
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EXTENSIONS
| More terms from Terryjames Morris (trm5002(AT)psu.edu), Mar 09 2007
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