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Search: id:A107785
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| A107785 |
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Sequence obtained using characteristic polynomial that is Laplace transform of the tribonacci characteristic polynomial: -s^4*L(t^3-t^2-t-1)=s^3+s^2+2*s-6. |
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+0
1
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| 0, 1, 1, 3, 7, 5, 37, 69, 35, 395, 739, 261, 4109, 8021, 1763, 42459, 87059, 8437, 437309, 942789, 17549, 4491883, 10183715, 1305243, 46013485, 109726261, 25530749, 470002683, 1179421747, 392600875, 4786258717, 12647990949
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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two methods given ( first): a(n) = -a(n-1)-2a(n-2)+6*a(n-3)
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MATHEMATICA
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(*first method*) F[1] = 0; F[2] = 1; F[3] = 1; F[n__] := F[n] = -F[n - 1] - 2*F[n - 2] + 6*F[n - 3] a = Table[Abs[F[n]], {n, 1, 50}] (*second method*) M = {{0, 1, 0}, {0, 0, 1}, {6, -2, -1}} v[1] = {0, 1, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 50}] Det[M - x*IdentityMatrix[3]]
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CROSSREFS
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Cf. A000045, A000213.
Adjacent sequences: A107782 A107783 A107784 this_sequence A107786 A107787 A107788
Sequence in context: A108974 A106853 A083778 this_sequence A001663 A085052 A016666
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 11 2005
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