Search: id:A008861
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%I A008861
%S A008861 1,2,4,8,16,32,64,128,256,511,1013,1981,3797,7099,12911,22819,39203,
%T A008861 65536,106762,169766,263950,401930,600370,880970,1271626,1807781,
%U A008861 2533987,3505699,4791323,6474541,8656937,11460949,15033173,19548046
%N A008861 Sum C(n,k), k=0..8.
%C A008861 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]
%D A008861 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 72, Problem 2.
%F A008861 a(n)=sum(binomial(n+1, 2k), k=0..4), compare A008859.
%F A008861 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+1\
               5980n^2+25584n+40320)/8! [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Jan 24 2009]
%e A008861 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]
%Y A008861 Cf. A008859, A008860, A008862, A008863, A006261, A000127.
%Y A008861 Sequence in context: A009694 A097000 A054046 this_sequence A145115 A104144 
               A123464
%Y A008861 Adjacent sequences: A008858 A008859 A008860 this_sequence A008862 A008863 
               A008864
%K A008861 nonn
%O A008861 0,2
%A A008861 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy

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