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A052942
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Expansion of 1/((1+x)(1-2x+2x^2-2x^3)).
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5
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1, 1, 1, 1, 3, 5, 7, 9, 15, 25, 39, 57, 87, 137, 215, 329, 503, 777, 1207, 1865, 2871, 4425, 6839, 10569, 16311, 25161, 38839, 59977, 92599, 142921, 220599, 340553, 525751, 811593, 1252791, 1933897, 2985399, 4608585, 7114167, 10981961
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=4, 3*a(n-4) equals the number of 3-colored compositions of n with all parts >=4, such that no adjacent parts have the same color.-Milan Janjic, Nov 27 2011
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 933
Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,2).
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FORMULA
| G.f.: -1/(-1+x+2*x^4)
Recurrence: {a(1)=1, a(0)=1, a(2)=1, a(3)=1, 2*a(n)+a(n+3)-a(n+4)=0}
Sum(1/539*(27+72*_alpha^3+96*_alpha^2+128*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+2*_Z^4))
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MAPLE
| spec := [S, {S=Sequence(Union(Z, Prod(Union(Z, Z), Z, Z, Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
seq(add(binomial(n-3*k, k)*2^k, k=0..floor(n/3)), n=0..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2007
with(combstruct): SeqSeqSeqL := [T, {T=Sequence(S), S=Sequence(U, card >= 1), U=Sequence(Z, card >3)}, unlabeled]: seq(count(SeqSeqSeqL, size=j), j=4..43); ; # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2009]
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CROSSREFS
| Sequence in context: A018388 A100866 A102633 * A117913 A064411 A146556
Adjacent sequences: A052939 A052940 A052941 * A052943 A052944 A052945
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 06 2000
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