A039301 Number of distinct quadratic residues mod 4^n.

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

Offset

0,2

Comments

Number of distinct n-digit suffixes of base 4 squares.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..170

Index entries for linear recurrences with constant coefficients, signature (5, -4).

Formula

a(n) = floor((4^n+10)/6).

a(n) = A007583(n-1)+1 = A020988(n-2)+2 = A083584(n-2)+3. - Ralf Stephan, Jun 14 2003

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

Prog

(Magma) [Floor((4^n+10)/6): n in [0..40] ]; // Vincenzo Librandi, Apr 28 2011

Crossrefs

Sequence in context: A275780 A334272 A348926 * A346505 A180205 A131529

Adjacent sequences: A039298 A039299 A039300 * A039302 A039303 A039304

Keyword

nonn,easy

Author

David W. Wilson

Status

approved