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A132262
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First term in a sum partition of the even-indexed Fibonacci numbers.
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2
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OFFSET
| 0,2
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COMMENTS
| This is the number in the center of the 3-regular tree when the exceptional representations of the 3-Kronecker quiver, whose dimension vector is given by subsequent even-indexed Fibonacci numbers are drawn into the 3-regular tree (the universal cover of the quiver).
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REFERENCES
| Ph. Fahr and C. M. Ringel, A Partition Formula for Fibonacci Numbers, preprint, 2007.
Philipp Fahr and Claus Michael Ringel, Categorification of the Fibonacci Numbers Using Representations of Quivers, http://www.mathematik.uni-bielefeld.de/~ringel/opus/fr-zwei.pdf
Mike Hirschhorn, Paper submitted to J. Int. Sequences, 2009.
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LINKS
| Ph. Fahr and C. M. Ringel, A Partition Formula for Fibonacci Numbers, preprint, 2007.
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FORMULA
| \frac{3\sqrt{1-6q+q^2}-(1+q)}{2(1-7q+q^2)}=1+2q+7q^2+29q^3+130q^4+... [From Mike Hirschhorn, Sep 03 2009]
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EXAMPLE
| a(3)=29 because 377=29+6*18+24*6+96*1
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CROSSREFS
| Cf. A110122.
Sequence in context: A150664 A193040 A200755 * A007852 A110576 A074600
Adjacent sequences: A132259 A132260 A132261 * A132263 A132264 A132265
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KEYWORD
| nonn,more
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AUTHOR
| Ph. Fahr and C. M. Ringel (philfahr(AT)math.uni-bielefeld.de), Aug 19 2007
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