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Search: id:A122194
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| A122194 |
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Numbers that are the sum of exactly two sets of Fibonacci numbers. |
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+0
2
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| 3, 5, 6, 9, 10, 15, 17, 25, 28, 41, 46, 67, 75, 109, 122, 177, 198, 287, 321, 465, 520, 753, 842, 1219, 1363, 1973, 2206, 3193, 3570, 5167, 5777, 8361, 9348, 13529, 15126, 21891, 24475, 35421, 39602, 57313, 64078, 92735, 103681, 150049, 167760, 242785
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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J. Berstel, An Exercise on Fibonacci Representations, RAIRO/Informatique Theorique, Vol. 35, No 6, 2001, pp. 491-498, in the issue dedicated to Aldo De Luca on the occasion of his 60-th anniversary.
M. Bicknell-Johnson & D.C. Fielder, 'The number of Representations of N Using Distinct Fibonacci Numbers, Counted by Recursive Formulas' Fibonacci Quart. 37.1 (1999) pgs 47 ff
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LINKS
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Ron Knott Sumthing about Fibonacci Numbers
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FORMULA
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a(2n-1) =A000032(n+2)-1, a(2n)=2 A000045(n+4) - 1. a(2n-1) = A001610(n+2), a(2n)=A001595(n+2). a(1)=3,a(2)=5,a(3)=6,a(4)=9,a(n)=a(n-2)+a(n-4)+1,n>4. GF: (3+2*x-2*x^2+x^3-3*x^4)/(x^5-x^4+x^3-x^2-x+1)
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EXAMPLE
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a(1)=3 as 3 is sum of just 2 Fibonacci sets {3=fib(4)} and {1=fib(2),2=fib(3)};
a(2)=5 as 5 is sum of Fibonacci sets {5} and {2,3} only.
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MAPLE
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fib:=fibonacci[combinat]: lucas:=n->fib(n-1)+fib(n+1): a:=n -> if n mod 2 = 0 then 2 *fib(n/2+3) -1 else lucas((n+1)/2+2)-1 fi;
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CROSSREFS
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Cf. A000045, A000071, A013583, A000119, A122195.
Sequence in context: A050083 A081175 A094598 this_sequence A053091 A047271 A047445
Adjacent sequences: A122191 A122192 A122193 this_sequence A122195 A122196 A122197
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KEYWORD
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nonn
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AUTHOR
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Ron Knott (enquiry(AT)ronknott.com), Aug 25 2006
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