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A108136
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a(1) = 1; a(2) = 1; a(3) = 1; a(n) = 3*a(n - 1) + 2*a(n - 2) + a(n - 3).
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0
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1, 1, 1, 6, 21, 76, 276, 1001, 3631, 13171, 47776, 173301, 628626, 2280256, 8271321, 30003101, 108832201, 394774126, 1431989881, 5194350096, 18841804176, 68346102601, 247916266251, 899282808131, 3262027059496, 11832563061001
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Length of steps in the 3-symbol substitution 1->{2}, 2->{3}, 3->{1,2,2,3,3,3} with characteristic polynomial: x^3-3*x^2-2*x-1.
No term is divisible by 5. [From Vladimir Joseph Stephan Orlovsky, Mar 24 2011]
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FORMULA
| M = {{0, 1, 0}, {0, 0, 1}, {1, 2, 3}}; v[n] = M.v[n - 1]; a(n) = v[n][[1]]
G.f.: x(1-2x-4x^2)/(1-3x-2x^2-x^3). a(n)=A108153(n)-2*A108153(n-1)-4*A108153(n-2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 14 2008]
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MATHEMATICA
| LinearRecurrence[{3, 2, 1}, {1, 1, 1}, 30]
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CROSSREFS
| Sequence in context: A200249 A027281 A006814 * A054625 A192733 A192144
Adjacent sequences: A108133 A108134 A108135 * A108137 A108138 A108139
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 05 2005
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