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A095898
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The (1,1)-term of the 3 X 3 matrix M^n, where M = [1,2,3 / 4,7,11 / 6,10,16].
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1
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1, 27, 649, 15603, 375121, 9018507, 216819289, 5212681443, 125321173921, 3012920855547, 72435421707049, 1741463041824723, 41867548425500401, 1006562625253834347, 24199370554517524729, 581791455933674427843, 13987194312962703792961, 336274454967038565458907
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 24*a(n-1) + a(n-2) for n>=3; a(1)=1, a(2)=27 (follows from the minimal polynomial of the matrix M).
a(n) = (-12 - sqrt(145))^(-n)*(87+7*sqrt(145) + (-289-24*sqrt(145))^n*(87-7*sqrt(145))) / 58. - Colin Barker, Mar 02 2017
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EXAMPLE
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a(4)=15603 because M^4 = [15603,26590,42193 / 56642,96527,153169 / 82078,139874,221952]. Alternatively, a(4) = 24*649+27 = 15603.
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MAPLE
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a[1]:=1: a[2]:=27: for n from 3 to 18 do a[n]:=24*a[n-1]+a[n-2] od: seq(a[n], n=1..18);
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PROG
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(PARI) Vec(x*(1 + 3*x) / (1 - 24*x - x^2) + O(x^30)) \\ Colin Barker, Mar 02 2017
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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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EXTENSIONS
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STATUS
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approved
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