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A052987
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Expansion of (1-2x^2)/(1-2x-2x^2+2x^3).
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4
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1, 2, 4, 10, 24, 60, 148, 368, 912, 2264, 5616, 13936, 34576, 85792, 212864, 528160, 1310464, 3251520, 8067648, 20017408, 49667072, 123233664, 305766656, 758666496, 1882398976, 4670597632, 11588660224, 28753717760, 71343560704
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Form the graph with matrix A=[1,1,1,1;1,0,0,0;1,0,0,0;1,0,0,1]. Then the sequence 1,1,2,4,... with g.f. (1-x-2x^2)/(1-2x-2x^2+2x^3) counts closed walks of length n at the degree 3 vertex. - Paul Barry (pbarry(AT)wit.ie), Oct 02 2004
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), May 27 2009: (Start)
Equals INVERT transform of the Jacobsthal sequence A001045 prefaced with a 1:
[1, 1, 1, 3, 5, 11, 21, 43,...]. (End)
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1061
Index to sequences with linear recurrences with constant coefficients, signature (2,2,-2).
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FORMULA
| G.f.: -(-1+2*x^2)/(1-2*x-2*x^2+2*x^3)
Recurrence: {a(0)=1, a(2)=4, a(1)=2, 2*a(n)-2*a(n+1)-2*a(n+2)+a(n+3)=0}
Sum(1/37*(6+7*_alpha+4*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(2*_Z^3-2*_Z^2-2*_Z+1))
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MAPLE
| spec := [S, {S=Sequence(Union(Prod(Sequence(Prod(Union(Z, Z), Z)), Z), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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CROSSREFS
| Cf. A077847.
Cf. A052528, A077937.
A001045 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 27 2009]
Sequence in context: A065161 A191758 A038373 * A100087 A088354 A055919
Adjacent sequences: A052984 A052985 A052986 * A052988 A052989 A052990
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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 05 2000
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