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Search: id:A074058
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| 4, -1, -1, -1, 7, -6, -1, -1, 15, -19, 4, -1, 31, -53, 27, -6, 63, -137, 107, -39, 132, -337, 351, -185, 303, -806, 1039, -721, 791, -1915, 2884, -2481, 2303, -4621, 7683, -7846, 7087, -11545, 19987, -23375, 22020, -30177, 51519, -66737, 67415, -82374, 133215, -184993, 201567, -232163, 348804
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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These numbers are obtained taking as characteristic polynomial the reflected ch.p. of the tetranacci generalized sequence and imposing initial conditions such that the coefficients of the generalized Binet's formula for the two sequences are the same. Also a(n) is the trace of A^(-n), where A is the tetramatrix ((1,1,0,0), (1,0,1,0),(1,0,0,1),(1,0,0,0)).
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REFERENCES
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R. L. Graham, D. E. Knuth and O. Patashnik, "Concrete Mathematics", Addison-Wesley, Reading, MA, 1998.
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FORMULA
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a(n)=-a(n-1)-a(n-2)-a(n-3)+a(n-4), a(0)=4, a(1)=-1, a(2)=-1, a(3)=-1. G.f.: (4+3x+2x^2+x^3)/(1+x+x^2+x^3-x^4)
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MATHEMATICA
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CoefficientList[Series[(4+3*x+2*x^2+x^3)/(1+x+x^2+x^3-x^4), {x, 0, 1}], x]
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CROSSREFS
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Cf. A073817.
Sequence in context: A063928 A131299 A073937 this_sequence A088440 A057521 A084885
Adjacent sequences: A074055 A074056 A074057 this_sequence A074059 A074060 A074061
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KEYWORD
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easy,sign
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Aug 16 2002
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