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A008863
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Sum C(n,k), k=0..10.
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8
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1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2047, 4083, 8100, 15914, 30827, 58651, 109294, 199140, 354522, 616666, 1048576, 1744436, 2842226, 4540386, 7119516, 10970272, 16628809, 24821333, 36519556, 53009102, 75973189, 107594213
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) is the number of compositions (ordered partitions) of n+1 into eleven or fewer parts. [From Geoffrey Critzer, Jan 24 2009]
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 72, Problem 2.
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FORMULA
| a(n) = sum(binomial(n+1, 2k), k=0..5), compare A008859.
G.f.: (1-9x+37x^2-91x^3+148x^4-166x^5+130x^6-70x^7+25x^8-5x^9+x^10) / (1-x)^11. a(n) = (n^10 -35n^9 +600n^8 -5790n^7 +36813n^6 -140595n^5 +408050n^4 -382060n^3 +1368936n^2 +2342880n +3628800)/10! [From Geoffrey Critzer, Jan 24 2009]
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EXAMPLE
| a(11) = 2047 because there are 2^11=2048 compositions of 12 into any size parts but one of the compositions (1+1+...+1=12) has more than eleven parts. [From Geoffrey Critzer, Jan 24 2009]
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CROSSREFS
| Cf. A008859, A008860, A008861, A008862, A006261, A000127.
Sequence in context: A194633 A113010 A056767 * A145117 A172320 A168082
Adjacent sequences: A008860 A008861 A008862 * A008864 A008865 A008866
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
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