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Search: id:A137356
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| A137356 |
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Sum_{k <= n/2 } binomial(n-2k, 3k). |
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+0
9
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| 1, 1, 1, 1, 1, 2, 5, 11, 21, 36, 58, 92, 149, 250, 431, 750, 1299, 2227, 3784, 6401, 10828, 18364, 31236, 53228, 90741, 154603, 263178, 447702, 761403, 1295022, 2203162, 3749001, 6380241, 10858285, 18478155, 31443013, 53501860, 91034937, 154900529, 263576791
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OFFSET
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0,6
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
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FORMULA
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Let A_n=\sum_{k<=n/2}{n-2k\choose3k} (the present sequence), B_n=\sum_{k<=n/2}{n-2k\choose3k+1} (A137357), C_n=\sum_{k<=n/2}{n-2k\choose3k+2} (A137358).
Then A_n=A_{n-1}+C_{n-3}+\delta_{n0}, B_n=B_{n-1}+A_{n-1}, C_n=C_{n-1}+B_{n-1};
so the generating functions are A = (1-z)^2/p(z), B=z(1-z)/p(z), C=z^2/p(z),
where p(z)=(1-z)^3-z^5=1-3z+3z^2-z^3-z^5.
The growth ratio is the real root of r^2(r-1)^3=1, approximately 1.70161.
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CROSSREFS
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Cf. A137357-A137361, A136444, A137402.
Sequence in context: A050407 A113032 A100134 this_sequence A103198 A003522 A112805
Adjacent sequences: A137353 A137354 A137355 this_sequence A137357 A137358 A137359
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KEYWORD
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nonn
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AUTHOR
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D. E. Knuth, Apr 11 2008
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