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A039301
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Number of distinct quadratic residues mod 4^n.
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9
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1, 2, 4, 12, 44, 172, 684, 2732, 10924, 43692, 174764, 699052, 2796204, 11184812, 44739244, 178956972, 715827884, 2863311532, 11453246124, 45812984492, 183251937964, 733007751852, 2932031007404, 11728124029612, 46912496118444
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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 4 squares.
a(n) = A007583(n-1)+1 = A020988(n-2)+2 = A083584(n-2)+3. - Ralf Stephan, Jun 14 2003
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..170
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FORMULA
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a(n) = floor((4^n+10)/6).
Also, a(0)=1 and, for n>0, a(n) = (4^n+8)/6. - Bruno Berselli, Jul 27 2010
G.f.: (1-3*x-2*x^2)/((1-x)*(1-4*x)). - Bruno Berselli, Jul 27 2010
a(n)-5*a(n-1)+4*a(n-2) = 0 for n>1. - Bruno Berselli, Jul 27 2010
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=4*a[n-1]-1 od: seq(a[n]+1, n=0..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008
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MATHEMATICA
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f[n_]:=4^n; lst={}; Do[a=f[n]; Do[a-=f[m], {m, n-1, 1, -1}]; AppendTo[lst, a], {n, 30}]; lst [From Vladimir Joseph Stephan Orlovsky, Feb 10 2010]
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PROG
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(MAGMA) [Floor((4^n+10)/6): n in [0..40] ]; // Vincenzo Librandi, Apr 28 2011
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CROSSREFS
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Sequence in context: A096802 A139669 A179973 * A180205 A131529 A165901
Adjacent sequences: A039298 A039299 A039300 * A039302 A039303 A039304
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KEYWORD
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nonn,easy
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AUTHOR
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David W. Wilson
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STATUS
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approved
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