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Search: id:A074062
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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
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OFFSET
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0,1
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COMMENT
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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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M. Catalani, Polymatrix and Generalized Polynacci Numbers
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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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CROSSREFS
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Cf. A074058, A074048, A061084.
Sequence in context: A046601 A101025 A028315 this_sequence A094635 A075463 A026518
Adjacent sequences: A074059 A074060 A074061 this_sequence 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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