Search: id:A097895
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%I A097895
%S A097895 0,0,2,3,11,20,51,99,222,441,935,1872,3863,7751,15774,31653,63939,
%T A097895 128232,257963,517011,1037630,2078417,4165647,8340192,16702191,33428943,
%U A097895 66912446,133891725,267921227,536022488,1072395555,2145272571
%N A097895 Number of compositions of n with at least 1 odd and 1 even part.
%F A097895 G.f.: x^3*(3*x-2)/((2*x-1)*(2*x^2-1)*(x^2+x-1)). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Sep 03 2004
%e A097895 n=4: 2+1+1, 1+2+1, 1+1+2. Total=3
%p A097895 G:=x^3*(3*x-2)/((2*x-1)*(2*x^2-1)*(x^2+x-1)): Gser:=series(G,x=0,37): 
               seq(coeff(Gser,x^n),n=1..35); (Deutsch)
%Y A097895 Cf. A000041 (partitions), A006477 (partitions of n with at least 1 odd 
               and 1 even part), A000009 (partitions into odd parts), A035363 (partitions 
               into even parts); A000079 (compositions). Compositions into odd parts 
               give Fibonacci numbers (A000045), into even parts gives 0, 1, 0, 
               2, 0, 4, 0, 8, 0, 16, 0, 32, 0, 64, ... (essentially A000079).
%Y A097895 Cf. A000045, A000041, A000009, A035363, A006477.
%Y A097895 Cf. A007179.
%Y A097895 Sequence in context: A129668 A086791 A004687 this_sequence A023182 A049083 
               A002778
%Y A097895 Adjacent sequences: A097892 A097893 A097894 this_sequence A097896 A097897 
               A097898
%K A097895 nonn
%O A097895 1,3
%A A097895 Dubois Marcel (dubois.ml(AT)club-internet.fr), Sep 03 2004
%E A097895 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 15 2005

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