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A092166
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Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (2,1) entry of M^n.
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3
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5, 25, 155, 925, 5555, 33325, 199955, 1199725, 7198355, 43190125, 259140755, 1554844525, 9329067155, 55974402925, 335846417555, 2015078505325, 12090471031955, 72542826191725, 435256957150355, 2611541742902125
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = (5*6^n - 5*(-1)^n)/7.
a(n) = 5*a(n-1) + 6*a(n-2).
G.f.: -5*x/((x+1)*(6*x-1)). (End)
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MATHEMATICA
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Table[ MatrixPower[{{1, 2}, {5, 4}}, n][[2, 1]], {n, 20}] (* Robert G. Wilson v, Apr 22 2004 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Apr 01 2004
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EXTENSIONS
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STATUS
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approved
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