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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, -5167, 9401, -9633, 6159, 39, -11133, 23969, -28667, 21951, -6081, -22305
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OFFSET
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0,1
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COMMENTS
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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.
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REFERENCES
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Mario Catalani, "Polymatrix and Generalized Polynacci Numbers", paper in progress.
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LINKS
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Table of n, a(n) for n=0..51.
Mario Catalani, Polymatrix and Generalized Polynacci Numbers, arXiv:math/0210201 [math.CO], 2002.
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FORMULA
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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).
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MATHEMATICA
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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]
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PROG
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(PARI) Vec((5+4*x+3*x^2+2*x^3+x^4)/(1+x+x^2+x^3+x^4-x^5) + O(x^55)) \\ Michel Marcus, Sep 14 2020
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CROSSREFS
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Cf. A074058, A074048, A061084.
Sequence in context: A046601 A101025 A028315 * A094635 A220054 A263152
Adjacent sequences: A074059 A074060 A074061 * A074063 A074064 A074065
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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 17 2002
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EXTENSIONS
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More terms from Michel Marcus, Sep 14 2020
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STATUS
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approved
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