A228920 Number of solutions to Sum_{i=1..n} x_i^2 == 0 (mod 4) with x_i in 0..3.
2, 4, 8, 32, 192, 1024, 4608, 18432, 69632, 262144, 1015808, 4063232, 16515072, 67108864, 270532608, 1082130432, 4311744512, 17179869184, 68585259008, 274341036032, 1098437885952, 4398046511104, 17600775979008, 70403103916032, 281543696187392
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (8,-24,32).
Programs
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Mathematica
Table[((2 + 2I)^n + (2 - 2I)^n + 4^n)/4, {n, 1, 30}] -
PARI
a(n)=((2+2*I)^n+(2-2*I)^n+4^n)/4 \\ Charles R Greathouse IV, Sep 15 2013
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PARI
Vec(-2*x*(12*x^2-6*x+1)/((4*x-1)*(8*x^2-4*x+1)) + O(x^100)) \\ Colin Barker, Nov 10 2014
Formula
a(n) = ((2+2i)^n + (2-2i)^n + 4^n)/4. - Charles R Greathouse IV, Sep 15 2013
G.f.: -2*x*(12*x^2-6*x+1) / ((4*x-1)*(8*x^2-4*x+1)). - Colin Barker, Nov 10 2014
Extensions
a(13)-a(25) from Charles R Greathouse IV, Sep 15 2013