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A074058 Reflected tetranacci numbers A073817. 8
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; text; internal format)
OFFSET

0,1

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)).

REFERENCES

R. L. Graham, D. E. Knuth and O. Patashnik, "Concrete Mathematics", Addison-Wesley, Reading, MA, 1998.

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..8998

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).

MATHEMATICA

CoefficientList[Series[(4+3*x+2*x^2+x^3)/(1+x+x^2+x^3-x^4), {x, 0, 1}], x]

CROSSREFS

Cf. A073817.

Sequence in context: A182665 A131299 A073937 * A308552 A088440 A300253

Adjacent sequences:  A074055 A074056 A074057 * A074059 A074060 A074061

KEYWORD

easy,sign

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Aug 16 2002

STATUS

approved

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Last modified May 30 11:52 EDT 2020. Contains 334724 sequences. (Running on oeis4.)