Search: id:A008860
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%I A008860
%S A008860 1,2,4,8,16,32,64,128,255,502,968,1816,3302,5812,9908,16384,26333,
%T A008860 41226,63004,94184,137980,198440,280600,390656,536155,726206,971712,
%U A008860 1285624,1683218,2182396,2804012,3572224,4514873,5663890,7055732
%N A008860 Sum C(n,k), k=0..7.
%C A008860 This is a general comment about sequences: A000012, A000027, A000124, 
               A000125, A000127, A006261, A008859, A008860, A008861, A008862, A008863. 
               Let j in {1, 2, ...11} index these 11 sequences respective to their 
               order above. Then a(n) in each sequence is the number of compositions 
               of (n+1) into j or fewer parts. From this we see that the ordinary 
               generating function for each sequence is the Sum x^i/(1-x)^(i+1), 
               i=0, j-1. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Jan 19 2009]
%D A008860 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 72, Problem 2.
%F A008860 a(n) = sum( binomial( n+1, 2k-1 ) for k=1..4 ) = ( n^6 -14*n^5 +112*n^4 
               -350*n^3 +1099*n^2 +364*n +3828 )*n/5040 +1.
%F A008860 G.f.:1-6x+16x^2-24x^3+22x^4-12x^5+4x^6/(1-x)^8 [From Geoffrey Critzer 
               (critzer.geoffrey(AT)usd443.org), Jan 19 2009]
%e A008860 a(8)=255 because there are 255 compositions of 9 into eight or fewer 
               parts. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Jan 
               23 2009]
%o A008860 (Other) sage: [binomial(n,1)+binomial(n,3)+binomial(n,5)+binomial(n,7) 
               for n in xrange(1, 36)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               May 17 2009]
%Y A008860 Cf. A008859, A008861, A008862, A008863, A006261, A000127.
%Y A008860 Sequence in context: A009641 A089889 A054045 this_sequence A145114 A079262 
               A087079
%Y A008860 Adjacent sequences: A008857 A008858 A008859 this_sequence A008861 A008862 
               A008863
%K A008860 nonn
%O A008860 0,2
%A A008860 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
%E A008860 Len Smiley's formula for A006261 copied by frank.ellermann(AT)t-online.de

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