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Search: id:A105476
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| A105476 |
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Number of compositions of n when each even part can be of two kinds. |
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+0
7
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| 1, 1, 3, 6, 15, 33, 78, 177, 411, 942, 2175, 5001, 11526, 26529, 61107, 140694, 324015, 746097, 1718142, 3956433, 9110859, 20980158, 48312735, 111253209, 256191414, 589951041, 1358525283, 3128378406, 7203954255, 16589089473, 38200952238
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OFFSET
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0,3
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COMMENT
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Row sums of A105475.
Starting (1, 3, 6, 15,...) = sum of (n-1)-th row terms of triangle A140168. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 10 2008
a(n) is also the number of compositions of n using 1's and 2's such that each run of like numbers can be grouped arbitrarily. For example, a(4) = 15 because 4 = (1)+(1)+(1)+(1) = (1+1)+(1)+(1) = (1)+(1+1)+(1) = (1)+(1)+(1+1) = (1+1)+(1+1) = (1+1+1)+(1) = (1)+(1+1+1) = (1+1+1+1) = (2)+(1)+(1) = (1)+(2)+(1) = (1)+(1)+(2) = (2)+(1+1) = (1+1)+(2) = (2)+(2) = (2+2). [From Martin J. Erickson (erickson(AT)truman.edu), Dec 09 2008]
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FORMULA
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G.f.=(1-z^2)/(1-z-3*z^2). a(n)=a(n-1)+3a(n-2) for n>=3.
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EXAMPLE
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a(3)=6 because we have (3),(1,2),(1,2'),(2,1),(2',1) and (1,1,1).
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MAPLE
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G:=(1-z^2)/(1-z-3*z^2): Gser:=series(G, z=0, 35): 1, seq(coeff(Gser, z^n), n=1..33);
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CROSSREFS
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Cf. A105475.
Cf. A006130, A105963.
Sequence in context: A006961 A034740 A152167 this_sequence A000599 A063832 A006647
Adjacent sequences: A105473 A105474 A105475 this_sequence A105477 A105478 A105479
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 09 2005
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