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A008862
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Sum C(n,k), k=0..9.
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8
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1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2036, 4017, 7814, 14913, 27824, 50643, 89846, 155382, 262144, 431910, 695860, 1097790, 1698160, 2579130, 3850756, 5658537, 8192524, 11698223, 16489546, 22964087, 31621024, 43081973, 58115146
(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 ten or fewer parts [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 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-1 ) for k=1..5 ), compare A008860.
G.f.: (1-8x+29x^2-62x^3+86x^4-80x^5+50x^6-20x^7+5x^8)/(1-x)^10 a(n)= (n^9-27n^8+366n^7-2646n^6+12873n^5-31563n^4+79064n^3+34236n^2+270576n+362880)/9! [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Jan 24 2009]
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EXAMPLE
| a(10)=1023 because there are (2^10)-1 compositions of 11 into ten or fewer parts. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Jan 24 2009]
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CROSSREFS
| Cf. A008859, A008860, A008861, A008863, A006261, A000127.
Sequence in context: A115213 A009714 A051535 * A145116 A172319 A122265
Adjacent sequences: A008859 A008860 A008861 * A008863 A008864 A008865
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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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