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Search: id:A008861
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| 1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1013, 1981, 3797, 7099, 12911, 22819, 39203, 65536, 106762, 169766, 263950, 401930, 600370, 880970, 1271626, 1807781, 2533987, 3505699, 4791323, 6474541, 8656937, 11460949, 15033173, 19548046
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OFFSET
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0,2
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COMMENT
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a(n)is the number of compositions (ordered partitions) of n+1 into nine or fewer parts. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Jan 24 2009]
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 72, Problem 2.
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FORMULA
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a(n)=sum(binomial(n+1, 2k), k=0..4), compare A008859.
G.f.: (1-7x+22x^2-40x^3+46x^4-34x^5+16x^6-4x^7+x^8)/(1-x)^9 a(n)= (n^8-20n^7+210n^6-1064n^5+3969n^4-4340n^3+15980n^2+25584n+40320)/8! [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Jan 24 2009]
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EXAMPLE
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a(9)=511 because all but one (namely 1+1+1+...+1=10) of the 2^9 compositions of 10 are in nine or fewer parts. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Jan 24 2009]
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CROSSREFS
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Cf. A008859, A008860, A008862, A008863, A006261, A000127.
Sequence in context: A009694 A097000 A054046 this_sequence A145115 A104144 A123464
Adjacent sequences: A008858 A008859 A008860 this_sequence A008862 A008863 A008864
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
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