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A122194 Numbers that are the sum of exactly two sets of Fibonacci numbers. 1
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; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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 60th 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

LINKS

Table of n, a(n) for n=1..46.

Ron Knott Sumthing about Fibonacci Numbers

FORMULA

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)

EXAMPLE

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.

MAPLE

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;

CROSSREFS

Cf. A000045, A000071, A013583, A000119, A122195.

Sequence in context: A182050 A094598 A263654 * A225005 A053091 A047271

Adjacent sequences:  A122191 A122192 A122193 * A122195 A122196 A122197

KEYWORD

nonn

AUTHOR

Ron Knott, Aug 25 2006

STATUS

approved

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Last modified June 28 20:39 EDT 2017. Contains 288840 sequences.