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A074062 Reflected (see A074058) pentanacci numbers A074048. 2
5, -1, -1, -1, -1, 9, -7, -1, -1, -1, 19, -23, 5, -1, -1, 39, -65, 33, -7, -1, 79, -169, 131, -47, 5, 159, -417, 431, -225, 57, 313, -993, 1279, -881, 339, 569, -2299, 3551, -3041, 1559, 799 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) is also the trace of A^(-n), where A is the pentamatrix ((1,1,0,0,0), (1,0,1,0,0),(1,0,0,1,0),(1,0,0,0,1),(1,0,0,0,0)).

a(n) is also the sum of determinants of 4th order principal minors of A^n.

REFERENCES

Mario Catalani, "Polymatrix and Generalized Polynacci Numbers", paper in progress.

LINKS

Table of n, a(n) for n=0..40.

Mario Catalani, Polymatrix and Generalized Polynacci Numbers, arXiv:math/0210201 [math.CO], 2002.

FORMULA

a(n) = -a(n-1)-a(n-2)-a(n-3)-a(n-4)+a(n-5), a(0)=5, a(1)=-1, a(2)=-1, a(3)=-1, a(4)=-1.

G.f.: (5+4x+3x^2+2x^3+x^4)/(1+x+x^2+x^3+x^4-x^5).

MATHEMATICA

CoefficientList[Series[5+4*x+3*x^2+2*x^3+x^4)/(1+x+x^2+x^3+x^4-x^5), {x, 0, 40}], x]

CROSSREFS

Cf. A074058, A074048, A061084.

Sequence in context: A046601 A101025 A028315 * A094635 A220054 A263152

Adjacent sequences:  A074059 A074060 A074061 * A074063 A074064 A074065

KEYWORD

easy,sign

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Aug 17 2002

STATUS

approved

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Last modified March 26 01:08 EDT 2019. Contains 321479 sequences. (Running on oeis4.)