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A123893
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G.f.: -(1+x^2)*(1+2*x^2)*(1+3*x^2)/(-1-6*x^2-11*x^4-6*x^6+4*x+18*x^3+22*x^5+6*x^7).
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0
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1, 4, 16, 58, 208, 750, 2708, 9772, 35256, 127210, 459012, 1656228, 5976040, 21562946, 77804232, 280736004, 1012961416, 3655002994, 13188110940, 47585806908, 171700784680, 619536821778, 2235434596432, 8065973894524, 29103931264328, 105013830473538
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OFFSET
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0,2
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COMMENTS
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Number of words of length n over (0,1,2,3} which have no factor iji with i>j. N. J. A. Sloane, May 21 2013
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LINKS
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Table of n, a(n) for n=0..25.
A. Burstein and T. Mansour, Words restricted by 3-letter generalized multipermutation patterns, Annals. Combin., 7 (2003), 1-14.
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
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a(0)=1, a(1)=4, a(2)=16, a(3)=58, a(4)=208, a(5)=750, a(6)=2708, a(n)= 4*a(n-1)-6*a(n-2)+18*a(n-3)-11*a(n-4)+22*a(n-5)-6*a(n-6)+6*a(n-7) Harvey P. Dale, May 20 2012
G.f. can be written 1/(1-x*(1+1/(1+x^2)+1/(1+2*x^2)+1/(1+3*x^2))) which looks more symmetrical. N. J. A. Sloane, May 21 2013
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MATHEMATICA
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CoefficientList[Series[-(1+x^2) (1+2 x^2) (1+3 x^2)/(-1-6 x^2-11 x^4-6 x^6+4 x+18 x^3+22 x^5+6 x^7), {x, 0, 40}], x] (* or *) LinearRecurrence[ {4, -6, 18, -11, 22, -6, 6}, {1, 4, 16, 58, 208, 750, 2708}, 40] Harvey P. Dale, May 20 2012
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CROSSREFS
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Cf. A005251, A123892, A123894, A225685.
Sequence in context: A123889 A180143 A224128 * A134762 A207276 A047123
Adjacent sequences: A123890 A123891 A123892 * A123894 A123895 A123896
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KEYWORD
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nonn,changed
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AUTHOR
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N. J. A. Sloane, Nov 20 2006
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STATUS
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approved
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