A228921 Number of solutions to Sum_{i=1..n} x_i^2 == 0 (mod 8) with x_i in 0..7.

2, 8, 32, 128, 3072, 32768, 294912, 2392064, 17825792, 134217728, 1040187392, 8313110528, 67645734912, 549755813888, 4432406249472, 35461397479424, 282574488338432, 2251799813685248, 17979214137393152, 143833163343331328, 1151795604700004352, 9223372036854775808

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: A331407 A160637 A183895 * A150829 A155084 A322251

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