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A039305
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Number of distinct quadratic residues mod 8^n.
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2
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1, 3, 12, 87, 684, 5463, 43692, 349527, 2796204, 22369623, 178956972, 1431655767, 11453246124, 91625968983, 733007751852, 5864062014807, 46912496118444, 375299968947543, 3002399751580332, 24019198012642647, 192153584101141164
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OFFSET
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0,2
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COMMENTS
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Number of distinct n-digit suffixes of base 8 squares.
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LINKS
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FORMULA
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a(n) = floor((8^n+10)/6).
G.f.: (1-5*x-13*x^2-4*x^3)/((1-x)*(1+x)*(1-8*x)). - Colin Barker, Mar 14 2012
a(n) = 8*a(n-1) + a(n-2) - 8*a(n-3) for n>0, a(0)=1. - Vincenzo Librandi, Apr 22 2012
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MATHEMATICA
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CoefficientList[Series[(1-5*x-13*x^2-4*x^3)/((1-x)*(1+x)*(1-8*x)), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 22 2012 *)
Join[{1}, LinearRecurrence[{8, 1, -8}, {3, 12, 87}, 30]] (* Harvey P. Dale, Feb 10 2015 *)
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PROG
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(Magma) I:=[1, 3, 12, 87]; [n le 4 select I[n] else 8*Self(n-1)+Self(n-2)-8*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Apr 22 2012
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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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STATUS
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approved
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