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A121551
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Number of parts in all the compositions of n into Fibonacci numbers (i.e. in all ordered sequences of Fibonacci numbers having sum n; only one 1 is considered as a Fibonacci number).
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1
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1, 3, 8, 19, 44, 98, 213, 457, 965, 2018, 4183, 8604, 17594, 35780, 72428, 146024, 293335, 587386, 1172836, 2335761, 4640947, 9201531, 18208325, 35967145, 70929855, 139667107, 274630886, 539309530, 1057789244, 2072370716
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)=Sum(k*A121548(n,k), k=1..n).
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FORMULA
| g.f.=Sum(z^fibonacci(i), i = 2 .. infinity)/[1-Sum(z^fibonacci(i), i=2.. infinity)]^2.
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EXAMPLE
| a(4)=19 because the compositions of 8 into Fibonacci numbers are [1,3],[2,2],[3,1],[1,1,2],[1,2,1],[2,1,1] and [1,1,1,1], having a total of 2+2+2+3+3+3+4=19 parts.
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MAPLE
| with(combinat): g:=sum(z^fibonacci(i), i=2..20)/(1-sum(z^fibonacci(i), i=2..20))^2: gser:=series(g, z=0, 48): seq(coeff(gser, z, n), n=1..35);
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CROSSREFS
| Cf. A000045, A121548.
Sequence in context: A102712 A054480 A191787 * A189391 A077850 A097550
Adjacent sequences: A121548 A121549 A121550 * A121552 A121553 A121554
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 07 2006
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