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A228921 Number of solutions to Sum(x_i^2, i=1...n) == 0 (mod 8). 4
2, 8, 32, 128, 3072, 32768, 294912, 2392064, 17825792, 134217728, 1040187392, 8313110528, 67645734912, 549755813888, 4432406249472, 35461397479424, 282574488338432, 2251799813685248, 17979214137393152, 143833163343331328, 1151795604700004352, 9223372036854775808 (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.: -2*x*(28672*x^6-9216*x^5+1280*x^4-64*x^3+48*x^2-12*x+1) / ((8*x-1)*(32*x^2-8*x+1)*(256*x^4+1)). - Colin Barker, Nov 10 2014

MATHEMATICA

a[n_]:= a[n]=16 a[n-1]-96 a[n-2] + 256 a[n-3]-256 a[n-4]+4096a[n-5]-24576a[n-6]+ 65536 a[n-7]; Do[a[i] = {2, 8, 32, 128, 3072, 32768, 294912}[[i]], {i, 1, 7}]; Array[a, 33]

PROG

(PARI) a(n)=my(v=vector(8, i, i==1)); for(i=1, n, v+=[2*v[8]+v[5], 2*v[1]+v[6], 2*v[2]+v[7], 2*v[3]+v[8], 2*v[4]+v[1], 2*v[5]+v[2], 2*v[6]+v[3], 2*v[7]+v[4]]); v[1]<<n \\ Charles R Greathouse IV, Sep 15 2013

(PARI) Vec(-2*x*(28672*x^6-9216*x^5+1280*x^4-64*x^3+48*x^2-12*x+1)/((8*x-1)*(32*x^2-8*x+1)*(256*x^4+1)) + O(x^100)) \\ Colin Barker, Nov 10 2014

CROSSREFS

Cf. A228920, A229138, A229136.

Sequence in context: A009117 A160637 A183895 * A150829 A155084 A150830

Adjacent sequences:  A228918 A228919 A228920 * A228922 A228923 A228924

KEYWORD

nonn,easy

AUTHOR

José María Grau Ribas, Sep 15 2013

EXTENSIONS

a(10)-a(22) from Charles R Greathouse IV, Sep 15 2013

STATUS

approved

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Last modified October 19 22:28 EDT 2018. Contains 316378 sequences. (Running on oeis4.)