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Search: id:A100967
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| A100967 |
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Greatest k such that binomial(2k + 1, k - n) < binomial(2k, k). |
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1
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| 3, 9, 18, 29, 44, 61, 81, 104, 130, 159, 191, 225, 263, 303, 347, 393, 442, 494, 549, 606, 667, 730, 797, 866, 938, 1013, 1091, 1172, 1255, 1342, 1431, 1524, 1619, 1717, 1818, 1922, 2029, 2138, 2251, 2366, 2485, 2606, 2730, 2857, 2987, 3119, 3255, 3394, 3535
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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From the formula, if we know k, we can estimate n as approximately 0.83 sqrt(k).
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FORMULA
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Round(0.3807 + 1.43869 n + 1.44276 n^2) is an exact fit for the first 50 terms.
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MATHEMATICA
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k=1; Table[While[Binomial[2k+1, k-n] < Binomial[2k, k], k++ ]; k, {n, 50}]
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CROSSREFS
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Cf. A003015 (numbers that occur 5 or more times in Pascal's triangle).
Sequence in context: A057681 A103312 A159794 this_sequence A134479 A045943 A127759
Adjacent sequences: A100964 A100965 A100966 this_sequence A100968 A100969 A100970
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Nov 23 2004
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