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

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (8,-24,32).

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

Mathematica

Table[((2 + 2I)^n + (2 - 2I)^n + 4^n)/4, {n, 1, 30}]

Prog

(PARI) a(n)=((2+2*I)^n+(2-2*I)^n+4^n)/4 \\ Charles R Greathouse IV, Sep 15 2013
(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

Crossrefs

Cf. A101990, A228921, A229136, A318609, A318610.

Column k = 0 of A330619.

Sequence in context: A298989 A074406 A186340 * A064378 A191650 A036544

Adjacent sequences: A228917 A228918 A228919 * A228921 A228922 A228923

Keyword

nonn,easy

Author

José María Grau Ribas, Sep 15 2013

Extensions

a(13)-a(25) from Charles R Greathouse IV, Sep 15 2013

Status

approved