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A074058
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Reflected tetranacci numbers A073817.
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7
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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; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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
| R. L. Graham, D. E. Knuth and O. Patashnik, "Concrete Mathematics", Addison-Wesley, Reading, MA, 1998.
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FORMULA
| 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
| 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
| Cf. A073817.
Sequence in context: A063928 A131299 A073937 * A088440 A203025 A057521
Adjacent sequences: A074055 A074056 A074057 * A074059 A074060 A074061
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KEYWORD
| easy,sign
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Aug 16 2002
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