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A076264
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Number of ternary (0,1,2) sequences without a consecutive '012'.
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23
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1, 3, 9, 26, 75, 216, 622, 1791, 5157, 14849, 42756, 123111, 354484, 1020696, 2938977, 8462447, 24366645, 70160958, 202020427, 581694636, 1674922950, 4822748423, 13886550633, 39984728949, 115131438424, 331507764639
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OFFSET
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0,2
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COMMENTS
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A transform of A000244 under the mapping g(x)->(1/(1+x^3))g(x/(1+x^3)). - Paul Barry, Oct 20 2004
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REFERENCES
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A. Tucker, Applied Combinatorics, 4th ed. p. 277
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LINKS
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Table of n, a(n) for n=0..25.
Index to sequences with linear recurrences with constant coefficients, signature (3,0,-1).
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FORMULA
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a(n) is asymptotic to g*c^n where c=cos(Pi/18)/cos(7*Pi/18) and g is the largest real root of : 81*x^3 - 81*x^2 - 9*x + 1 = 0. - Benoit Cloitre, Nov 06 2002
G.f.: 1/(1-3x+x^3). a(n) = 3*a(n-1)-a(n-3), n>0.
a(n)=sum{k=0..floor(n/3), binomial(n-2k, k)(-1)^k*3^(n-3k)} - Paul Barry, Oct 20 2004
a(n) = middle term in M^(n+1) * [1 0 0], where M = the 3X3 matrix [2 1 1 / 1 1 0 / 1 0 0]. Right term = A052536(n), left term = A052536(n+1). - Gary W. Adamson, Sep 05 2005
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PROG
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(PARI) a(n)=if(n<0, 0, polcoeff(1/(1-3*x+x^3)+x*O(x^n), n))
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CROSSREFS
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The g.f. corresponds to row 3 of triangle A225682.
Sequence in context: A077845 A171277 A000243 * A018919 A123941 A005774
Adjacent sequences: A076261 A076262 A076263 * A076265 A076266 A076267
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KEYWORD
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nonn,easy,changed
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AUTHOR
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John L. Drost, Nov 05 2002
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STATUS
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approved
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