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A229138 Number of solutions to Sum_{i=1...n} x_i^2 == 1 (mod 8) with x_i in 0..7. 8
4, 16, 96, 512, 2560, 24576, 229376, 2097152, 17956864, 142606336, 1107296256, 8589934592, 67612180480, 541165879296, 4363686772736, 35184372088832, 282583078273024, 2260595906707456, 18049582881570816, 144115188075855872, 1151793405676748800 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 26 16:44 EDT 2021. Contains 346294 sequences. (Running on oeis4.)