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Search: id:A052945
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| A052945 |
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Number of compositions of n when each odd part can be of two kinds. |
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+0
5
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| 1, 2, 5, 14, 38, 104, 284, 776, 2120, 5792, 15824, 43232, 118112, 322688, 881600, 2408576, 6580352, 17977856, 49116416, 134188544, 366609920, 1001596928, 2736413696, 7476021248, 20424869888, 55801782272, 152453304320
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1004
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FORMULA
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G.f.: (-1+x)*(1+x)/(-1+2*x+2*x^2)
Recurrence: {a(0)=1, a(1)=2, a(2)=5, 2*a(n)+2*a(n+1)-a(n+2)}
Sum(1/4*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z+2*_Z^2))
a(n)=((2+sqrt3)(1+sqrt3)^n+(2-sqrt3)(1-sqrt3)^n)/2 offset 0. Lead w. one. a(n)=first binomial transform of 2,3,6,9,18... offset 0. Lead w. one. [From Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009]
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EXAMPLE
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a(3)=14 because we have (3),(3'),(1,2),(1',2),(2,1),(2,1'),(1,1,1),(1,1,1'),(1,1',1),(1,1',1'),(1',1,1),(1',1,1'),(1',1',1) and (1',1',1').
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MAPLE
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spec := [S, {S=Sequence(Prod(Union(Sequence(Prod(Z, Z)), Sequence(Z)), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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CROSSREFS
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Row sums of A105474.
Sequence in context: A148313 A084085 A052985 this_sequence A026288 A047086 A006574
Adjacent sequences: A052942 A052943 A052944 this_sequence A052946 A052947 A052948
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 05 2000
Better description from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 09 2005
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