A229138 Number of solutions to Sum_{i=1...n} x_i^2 == 1 (mod 8) with x_i in 0..7.

4, 16, 96, 512, 2560, 24576, 229376, 2097152, 17956864, 142606336, 1107296256, 8589934592, 67612180480, 541165879296, 4363686772736, 35184372088832, 282583078273024, 2260595906707456, 18049582881570816, 144115188075855872, 1151793405676748800

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (16,-96,256,-256,4096,-24576,65536).

Formula

G.f.: 4*x*(1 -12*x +56*x^2 -128*x^3 +128*x^4 -1024*x^5 +2048*x^6)/((1-8*x)*(1+256*x^4)*(1-8*x+32*x^2)). - Colin Barker, Nov 10 2014

Maple

seq(coeff(series(4*x*(1 -12*x +56*x^2 -128*x^3 +128*x^4 -1024*x^5 +2048*x^6)/( (1-8*x)*(1+256*x^4)*(1-8*x+32*x^2)), x, n+1), x, n), n = 1..30); # G. C. Greubel, Dec 21 2019

Mathematica

a[n_]:= a[n]= 16a[n-1] -96a[n-2] +256a[n-3] -256a[n-4] +4096a[n-5] -24576 a[n-6] +65536 a[n-7]; Do[a[i]={4, 16, 96, 512, 2560, 24576, 229376}[[i]], {i, 7}]; Array[a, 33]

Prog

(PARI) Vec(4*x*(1-12*x+56*x^2-128*x^3+128*x^4-1024*x^5+2048*x^6)/((1-8*x)*(1+256*x^4)*(1-8*x+32*x^2)) + O(x^30)) \\ Colin Barker, Nov 10 2014
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 4*x*(1 -12*x +56*x^2 -128*x^3 +128*x^4 -1024*x^5 +2048*x^6)/((1-8*x)*(1+256*x^4)*(1-8*x+32*x^2)) )); // G. C. Greubel, Dec 21 2019
(Sage)
def A229138_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 4*x*(1 -12*x +56*x^2 -128*x^3 +128*x^4 -1024*x^5 +2048*x^6)/( (1-8*x)*(1+256*x^4)*(1-8*x+32*x^2)) ).list()
a=A229138_list(30); a[1:] # G. C. Greubel, Dec 21 2019

Crossrefs

Cf. A101990, A228920, A228921, A229136, A318609, A318610, A330607, A330619.

Sequence in context: A096243 A263565 A131928 * A098580 A317998 A027745

Adjacent sequences: A229135 A229136 A229137 * A229139 A229140 A229141

Keyword

nonn,easy

Author

José María Grau Ribas, Sep 15 2013

Status

approved