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A052986
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Expansion of ( 1-2*x ) / ( (x-1)*(2*x^2+3*x-1) ).
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0
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1, 2, 7, 24, 85, 302, 1075, 3828, 13633, 48554, 172927, 615888, 2193517, 7812326, 27824011, 99096684, 352938073, 1257007586, 4476898903, 15944711880, 56787933445, 202253224094, 720335539171, 2565513065700, 9137210275441
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1060
Index to sequences with linear recurrences with constant coefficients, signature (4,-1,-2).
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FORMULA
| G.f.: (1-2*x)/(1-4*x+x^2+2*x^3)
Recurrence: {a(0)=1, a(1)=2, -2*a(n)-3*a(n+1)+a(n+2)+1=0}
Sum(-1/136*(-13-27*_alpha+6*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-4*_Z+_Z^2+2*_Z^3))
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MAPLE
| spec := [S, {S=Sequence(Union(Prod(Union(Sequence(Union(Z, Z)), Z), Z), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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MATHEMATICA
| Join[{a=1, b=2}, Table[c=3*b+2*a-1; a=b; b=c, {n, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 17 2011*)
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CROSSREFS
| Sequence in context: A088854 A000777 A144170 * A053368 A141753 A014300
Adjacent sequences: A052983 A052984 A052985 * A052987 A052988 A052989
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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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