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A097895
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Number of compositions of n with at least 1 odd and 1 even part.
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0
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0, 0, 2, 3, 11, 20, 51, 99, 222, 441, 935, 1872, 3863, 7751, 15774, 31653, 63939, 128232, 257963, 517011, 1037630, 2078417, 4165647, 8340192, 16702191, 33428943, 66912446, 133891725, 267921227, 536022488, 1072395555, 2145272571
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| 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
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EXAMPLE
| n=4: 2+1+1, 1+2+1, 1+1+2. Total=3
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MAPLE
| 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)
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MATHEMATICA
| e=(1-x^2)/(1-2x^2); o=(1-x^2)/(1-x-x^2); nn=30; Drop[CoefficientList[Series[(1-x)/(1-2x)-(o+e), {x, 0, nn}], x], 1] (* Geoffrey Critzer, Jan 18 2012 *)
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CROSSREFS
| 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).
Cf. A000045, A000041, A000009, A035363, A006477.
Cf. A007179.
Sequence in context: A129668 A086791 A004687 * A023182 A049083 A002778
Adjacent sequences: A097892 A097893 A097894 * A097896 A097897 A097898
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KEYWORD
| nonn
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AUTHOR
| Dubois Marcel (dubois.ml(AT)club-internet.fr), Sep 03 2004
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 15 2005
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